zotero/storage/T6AIFP6P/.zotero-ft-cache

Supercollider physics
E. Eichten
Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510
l. Hinchliffe
Laivrence Berkeley Laboratory, Berkeley, California 94720
K. Lane
The Ohio State University, Columbus, Ohio 43210
C. Quigg
Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510
Eichten et al. summarize the motivation for exploring the 1-TeV (=10' eV) energy scale in elementary particle interactions and explore the capabilities of proton-(anti)proton colliders with beam energies between 1 and 50 TeV. The authors calculate the production rates and characteristics for a number of conventional processes, and discuss their intrinsic physics interest as well as their role as backgrounds to more exotic phenomena. The authors review the theoretical motivation and expected signatures for several new phenomena which may occur on the 1-TeV scale. Their results provide a reference point for the choice of machine parameters and for experiment design.
CONTENTS
I. Introduction A. Where we stand B. The importance of the 1-TeV scale C. The purpose and goals of this paper II. Preliminaries A. Parton model ideas B. Q -dependent parton distributions C. Parton-parton luminosities III. Physics of Hadronic Jets A. Generalities B. Two-jet final states C. Multijet phenomena D. Summary IV. Electroweak Phenomena A. Dilepton production B. Intermediate boson production C. Pair production of gauge bosons
1. Production of 8'+ W pairs 2. Production of 8'+—Z pairs 3. Production of ZOZ pairs
4. W —y production
5. Z y production
D. Production of Higgs bosons E. Associated production of Higgs bqsons and gauge bosons F. Summary V. Minimal Extensions of the Standard Model A. Pair production of heavy quarks B. Pair production of heavy leptons C. New electroweak gauge bosons D. Summary VI. Technicolor A. Motivation B. The minimal technicolor model C. The Farhi-Susskind model D. Single production of technipions E. Pair production of technipions
F. Summary VII. Supersymmetry A, Superpartner spectrum and elementary cross sections
579 580 581 582 583 583 585 592 596 596 598 607 617 617 618 621 624 625 628 630 631 632 633
640 642 642 643 645 648 650 650 650 652 655 660 662 665 666
667
1. Ciaugino pair production 2. Associated production of squarks and gauginos 3. Squark pair production B. Production and detection of strongly interacting superpartners C. Production and detection of color singlet superpartners D. Summary VIII. Composite guarks and Leptons A. %manifestations of compositeness B. Signals for compositeness in high-p& jet production C. ' Signals for composite quarks and leptons in leptonpair production D. Summary IX. Summary and Conclusions Acknowledgments Appendix. Parametrizations of the Parton Distributions References
668 669 670
672
676 683 684 685 687
690 695 696 698 698 703
I ~ INTRODUCTION
For expositions of the current paradigm, see the textbooks by Okun (1981), Perkins (1982), Aitchison and Hey (1982), Leader and Predazzi (1982), Quigg {1983), and Halzen and Martin (1984) and the summer school proceedings edited by Cxaillard and Stor@ (1983).
The physics of elementary particles has undergone a re
markable development during the past decade. A host of new experimental results made accessible by a new generation of particle accelerators and the accompanying rapid convergence of theoretical ideas have brought to the subject a new coherence. Our current outlook has been shaped by the identification of quarks and leptons as fundamental constituents of matter and by the gauge theory
synthesis of the fundamental interactions. ' These
developments represent an important simplification of
Reviews of Modern Physics, Vol. 56, No. 4, October 1984 Copyright 1984 The American Physical Society


580 Eichten et al. : Supercollider physics
basic concepts and the evolution of a theoretical strategy with broad applicability.
One of the strengths of our current theoretical frame
work is that it defines the frontier of our ignorance —the energy scale of about 1 TeV on which new phenomena must occur, and where experimental guidance toward a more complete understanding must be found. It is to explore this realm that plans are being developed (Wojcicki et al., 1983) for the construction of a multi-TeV high
luminosity hadron-hadron collider. The physics capabilities of such a device and the demands placed upon ac
celerator parameters by the physics are the subject of this paper.
Three things are done in the remainder of this introductory section. First, we give a brief description of the present understanding of the strong, weak, and electromagnetic interactions. Second, we examine the incompleteness and shortcomings of this picture and explain why, in general terms, exploration of the 1-TeV scale is interesting and necessary. Finally, we describe the goals and contents of this paper.
A. Where we stand
The picture of the fundamental constituents of matter and the interactions among them that has emerged in recent years is one of great beauty and simplicity. All matter appears to be composed of quarks and leptons,
which are pointlike, structureless, spin- —, particles. If we leave aside gravitation, which is a negligible perturbation at the energy scales usually considered, the interactions among these particles are of three types: weak, elec
tromagnetic, and strong. All three of these interactions are described by gauge theories, and are mediated by spin-1 gauge bosons. The quarks experience all three interactions; the leptons participate only in the weak and electromagnetic interactions. The systematics of the charged-current (P-decay) weak interactions suggest grouping the six known leptons into three families:
e
Similarly, the five known quarks appear in the doublets
c [t]
~ I y Ql (1.2)
M, &22.5 GeV/c (1.3)
Recently, the UA-1 Collaboration (Rubbia, 1984) has announced preliminary evidence for the top quark, with
where the primes denote generalized Cabibbo
(1963)—Kobayashi and Maskawa (1973) mixing among
the charge ——' , flavors. Symmetry considerations and the features of b-quark decay suggest the existence of a third
quark of charge + —,, designated t. Current experiments
set a lower limit on its mass of (Yamada, 1983)
30&M, &60 GeV/c . Each quark flavor comes in three distinguishable varieties, called colors. Color is what distinguishes the quarks from the leptons. Since the leptons are inert with respect to the strong interactions, it is natural to interpret color as a strong interaction charge. The theory of strong interactions, quantum chromodynamics (QCD) (Bardeen, Fritzsch, and Gell-Mann, 1973; Gross and Wilczek, 1973b; Weinberg, 1973) is based
upon the exact local color gauge symmetry SU(3), .
Strong interactions are mediated by an SU(3) octet of colored gauge bosons called gluons. The gauge symmetry is exact, and the gluons are massless particles. However, it is widely believed, if not yet rigorously proved, that in QCD quarks and gluons are permanently confined within color singlet hadrons. A crucial property of non-Abelian gauge theories in general and of QCD in particular is asymptotic freedom (Gross and Wilczek, 1973a; Politzer, 1973); the tendency of the coupling strength to diminish at short distances. This behavior suggests a resolution to the parton model paradox that quarks behave as free particles within hadrons, but can never be liberated. A unified description of the weak and electromagnetic
interactions is provided by the Glashow (1961)—Weinberg
(1967)—Salam (1968) theory based on the gauge group
SU(2)1.U(1)z. In this theory, unlike QCD, the local gauge invariance is spontaneously broken, or hidden, by the Higgs (1964) mechanism. This causes the intermedi
ate bosons 8'+, 8', and Z of the weak interactions to
acquire large masses, while leaving the photon massless. . A consequence of this form of spontaneous symmetry breaking is the existence of a scalar Higgs boson of unspecified mass. The SU(2)L, U(1)z model has a number of notable successes: the prediction and detailed description of the weak neutral current interactions first observed by Hasert et al. (1973a,1973b, 1974) and Benvenuti
et al. (1974), the prediction of charm (Cazzoli et al., 1975; Goldhaber et al., 1976; Peruzzi et al., 1976), and the
predictions of the masses of the charged (Arnison et al., 1983a; Banner et al., 1983) and neutral (Arnison et al.,
1983c; Bagnaia et al., 1983b) intermediate bosons.
The so-called "standard model" of QCD plus the SU(2)LU(1)z electroweak theory incorporates all the
principal systematics of elementary-particle phenomenology, and achieves a wide-ranging synthesis of elementary
phenomena. It is of great importance to continue to test the standard model, and to explore the predictions of unified theories of the strong, weak, and electromagnetic interactions (Georgi and Glashow, 1974; Pati and Salam, 1973a,1973b,1974), which seem a natural next step. The degree of current experimental support for the elec
troweak theory, for QCD, and for the idea of grand unifi
cation is rather different. For the electroweak theory the task is now to refine precise quantitative tests of very detailed predictions and to explore the Higgs sector. In the case of QCD, most comparisons of theory and experiment
are still at the qualitative level, either because a precise
theoretical analysis has not been carried out, or because of the difficulties of the required measurement. We find
ourselves in the curious position of having a plausible
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Eichten et al. : Supercollider physics 581
theory which we have not been able to exploit in full. So far as unified theories are concerned, we are only beginning to explore their consequences experimentally. Although the simplest model provides an elegant example of how unification might occur, no "standard" unified theory has yet been selected by experiment. Over the next decade, the vigorous experimental program at accelerators now operating or under construction will subject QCD and the electroweak theory to ever more stringent testing, and nonaccelerator experiments, such as searches for nucleon instability, will explore some of the dramatic consequences of unified theories. Surprises may well be encountered, but it is likely that our efforts to understand why the standard model works and to construct more complete descriptions of nature will remain unfulfilled. In order to explain what sort of experimental guidance will be required, we next consider why the standard model cannot be the final answer, and where new phenomena are to be expected.
B. The importance of the 1-TeV scale
It is essential to recognize that the current paradigm
leaves unanswered some central questions. Even if we go beyond what has been persuasively indicated by experi
ment, and suppose that the idea of a unified theory of the strong, weak, and electromagnetic interactions is correct, there are several areas in which accomplishments fall short of coinplete understanding. There are also a number of specific problems to be faced.
~ The most serious structural problem is associated
with the scalar, or Higgs, sector of the electroweak theory. This sector is responsible for the most obvious feature of electroweak symmetry, namely, that it is broken. Yet the dynamical nature of this sector is the least understood aspect of the theory. In the standard model, the interactions of the Higgs boson are not prescribed by
the gauge symmetry in the manner of those of the inter
mediate bosoris. Whereas the masses of the W and Z are specified by the theory, the mass of the Higgs boson is constrained only to lie within the range 7 GeV/c (Linde, 1976; Weinberg, 1976a) to 1 TeV/c (Veltman, 1977; Lee, Quigg, and Thacker, 1977). While the lower bound is
strictly valid only in the simplest version of the standard model with one elementary Higgs doublet, the upper
bound is fairly model independent. If the Higgs boson mass exceeds this bound, weak interactions must become strong on the TeV scale. This is perhaps the most compelling argument that new physics of some sort must
show up at or before the energy scale of —1 TeV is
reached. In a unified theory, the problem of the ambiguity of the Higgs sector is heightened by the requirement
that there be a dozen orders of magnitude between the
masses of W+—and Zo and those of the leptoquark bosons that would mediate proton decay.
0 No particular insight has been gained into the pattern
of quark and lepton masses or into the mixing between different quark flavors. This fact may be quantified by
noting that the number of apparently arbitrary parameters needed to specify the theory is 20 or more. This is at odds with our viewpoint, fostered by a history of repeated simplifications, that the world should be comprehensible in terms of a few simple laws. Much of the progress represented by the gauge theory synthesis is associated
with the reduction of ambiguity made possible by a guid
ing principle. Since so much of the dynamical origin of the inasses and mixing angles of quarks and leptons has to do with their coupling to the electroweak scalar sector, here again we have good reason to hope that a thorough study of 1-TeV physics will yield important answers.
~ The violation of CP invariance in the weak interaction does not arise gracefully. The currently most popular interpretation attributes this phenomenon to the possibility of complex couplings of quarks to the Higgs boson, but, at least in the simplest model, this scenario has a serious problem: large CP violations in the strong interactions. Once again, our experimental ignorance of the scalar sector is hindering our theoretical understanding.
~, The requirement that the electroweak theory be
anomaly free suggests grouping quark and lepton doublets
into fermion "generations. " Although this idea is supported by the explanation of charge quantization in unified theories, we do not know why generations repeat or how many there are. Indeed, with the large number of quarks and leptons that we now have, it is natural to ask whether these fermionic constituents are truly elementary.
If it should turn out that they are in fact composite structures, then the successes of the standard model imply that
their characteristic size is less than —10 cm, corresponding to an energy scale & 1 TeV.
~ Finally, we may ask what the origin of the gauge symmetries themselves is, why the weak interactions are left-handed, and whether there are new fundamental interactions to be discovered. Coven this list, it is not surprising that there are many directions of theoretical speculation departing from the current paradigm. Many of these have important implications which cannot yet be tested. Although theoretical speculation and synthesis is valuable and necessary, we cannot advance without new observations. The experimental clues needed to answer questions like those posed above can come from several sources, including
experiments at high-energy accelerators; experiments at low-energy accelerators and nuclear reactors; nonaccelerator experiments; deductions from astrophysical measurements.
However, according to our present knowledge of elementary particle physics, our physical intuition, and our past experience, most clues and information will come from experiments at the highest-energy accelerators. Since many of the questions we wish to pose are beyond
the reach of existing accelerators and those under construction, further progress in the field will depend on our ability to study phenomena at higher energies, or
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582 Eichten et af.: Supercollider physics
equivalently, on shorter scales of time and distance. What energy scale must we reach, and what sort of new instruments do we require'? Field theories with elementary scalars are notoriously unstable (Wilson, 1971) against large radiative corrections to masses. As a consequence, although the Higgs phenomena might possibly occur at less than 1 TeV, building a comprehensive theory in which this occurs proves to be a very difficult problem, unless some new physics intervenes. One possible solution to the Higgs mass problem involves introducing a complete new set of elementary particles whose spins differ by one-half unit from the known quarks, leptons, and gauge bosons. These postulated new
particles are consequences of a new "supersymmetry" which relates particles of integral and half-integral spin. The conjectured supersymmetry would stabilize the mass
of the Higgs boson at a value below 1 TeV/c, and the supersymmetric particles are likely themselves to have masses less than about 1 TeV/c . Up to the present, there is no experimental evidence for these superpartners. A second possible solution to the Higgs problem is based on the idea that the Higgs boson is not an elementary particle at all, but is in reality a composite object made
out of elementary constituents analogous to the quarks and leptons. Although they would resemble the usual quarks and leptons, these new constituents would be subject to a new type of strong interactions (often called
"technicolor" ) that would confine them within about
10 ' cm. Such new forces could yield new phenomena as rich and diverse as the conventional strong interactions, but on an energy scale a thousand times greateraround 1 TeV. The new phenomena would include a rich spectrum of technicolor-singlet bound states, akin to the spectrum of known hadrons. Again, there is no evidence yet for these new particles. We thus see that both general arguments such as unitarity constraints and specific conjectures for resolutions of the Higgs problem imply 1 TeV as an energy scale on
which new phenomena. crucial to our understanding of the fundamental interactions must occur. The dynamical origin of electroweak symmetry breaking is of course only one of the important issues that define the frontier of elementary particle physics. However, because of its immediacy and its fundamental significance it must guide our planning for future facilities.
Either an electron-positron collider with beams of 1—3
TeV or a proton-(anti)proton collider with beams of 5—20 TeV would allow an exploration of the TeV region for hard collisions. The higher beam energy required for protons simply ref1ects the fact that the proton's energy is shared among its quark and gluon constituents. The partitioning of energy among the constituents has been thoroughly studied in experiments on deeply inelastic scattering, so the rate of collisions among constituents of various energies may be calculated with some confidence. The physics capabilities of the electron-positron and proton-(anti)proton options are both attractive and somewhat complementary. The hadron machine reaches to
higher energy and provides a wider variety of constituent collisions, which allows for a greater diversity of phenom
ena. The simple initial state of the electron-positron machine represents a considerab1e measurement advantage. However, the results of the CERN protonantiproton collider (Banner et al., 1982; Arnison et al.,
1983b) indicate that hard collisions at very high energies are relatively easy to identify. Because the current state
of technology favors the hadron collider, it is the instru
ment of choice for the first exploration of the TeV re
gime. Some studies of the accelerator physics and technology required for a multi-TeV collider have already been carried out (Tigner, 1983; Diebold, 1983; Marx,
1984).
C. The purpose and goals of this paper
We have reviewed the principal rationale for a multiTeV hadron collider: it is a device to illuminate the physics of electroweak symmetry breaking. At the same time, it is necessary to anticipate that the supercollider will reveal more than this. Surprises and unexpected insights have always been encountered in each new energy regime, and we confidently expect the same result at TeV energies. No one knows what form these discoveries will take, but is essential that the supercollider provide the means to make them. Fortunately, both the conventional possibilities of the standard model and the new phenomena implied by existing speculations can serve the important
function of calibrating the capacity for discovery of a planned facility. They also help to fix the crucial parameters for a new machine: the energy per beam and the luminosity, or rate at which collisions occur. In any case, the expected phenomena are important as backgrounds for the unexpected, and for each other. Our principal goal in this paper is to set out the most obvious possibilities in enough detail that we may begin to assess the demands of the physics upon beam energy and luminosity, and to consider the relative merits of the pp
and pp options. In addition, we intend to provide a refer
ence point for the design of detectors and experiments. Earlier work relevant to these issues has been reported in the Proceedings of the 1982 Snowmass Workshop (Donaldson, Gustafson, and Paige, 1982) and of the 1983 Berkeley Detector Workshop (Loken and Nemethy, 1983). We also wish to identify areas in which further work is required. Hard-scattering phenomena make the most stringent demands upon machine performance. Accordingly, we shall not discuss the low transverse momentum phenome
na known as "logs physics. " Some of these considerations are treated in the lectures by Cahn (1982) and Jacob (1983). For the same reason, we do not address the physics interest of the conjectured new state of matter known as quark-gluon plasma (McLerran, 1983). We also omit any discussion of fixed target physics with multi-TeV beams, for which the opportunities and concerns are rather different. This topic has been considered in the Snowmass (Pondrom, 1982), Diablerets (Amaldi, 1980),
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Eichten et al. : Supercollider physics 583
and Woodlands (McIntyre et aL, 1984) workshops. A detailed description of the material presented in this paper appears in the Table of Contents. A brief summary
is in order here. Section II is devoted to a review of the
renoraialization-group —improved-parton model and the nucleon structure functions required to make predictions
of production rates. The hard-scattering hadron jet phe
nomena predicted by QCD that provide a window on con
stituent interactions are taken up in Sec. III. In Sec. IV we discuss the standard electroweak theory, in particular
as it pertains to searches for heavy Higgs bosons. Sec
tions III and IV„ then, are concerned with processes which are intrinsically interesting as definitive tests of the standard model, and which produce the principal backgrounds to the new physics the supercollider is intended to explore. The four sections that follow concentrate on several of the more frequently discussed possibilities for new phys
ics. The simplest extensions of the standard SU(2)L,
U(1)r theory, new quark and lepton flavors and additional intermediate bosons are treated in Sec. V. We then
turn to more speculative possibilities: technicolor (Sec. VI), supersymmetry (Sec. VII), and quark-lepton compos
iteness (Sec. VIII). In each of these cases we review the motivations for the conjecture and discuss the expected experimental signatures. We also examine the potential backgrounds and assess the physics reach of the collider
as a function of energy and luminosity for pp and pp col
lisions. The reason for covering these proposals in some
detail is not that any one of them necessarily is correct. Rather, they provide a very wide range of experimental challenges which we must expect the supercollider to
meet if it is to explore thoroughly and effectively the
physics of the 1-TeV scale. Some tentative conclusions
from our study are given in Sec. IX.
A. Parton model ideas
The essence of the parton model is to regard a highenergy proton (or other hadron) as a collection of quasi
free partons which share its momentum. Thus we en
visage a proton of momentum P as being made of partons carrying longitudinal momenta x;P, where the momen
tum fractions x; satisfy
and
0(x;(1 (2.3)
xr. ——& ~ partons
(2.4)
reaction rates, as we shall document below. Two ingredients are therefore required in order to compute cross sections and experimental distributions: the elementary cross sections and the parton distributions. It
is straightforward to calculate the elementary cross sections, at least at low orders in perturbation theory, from the-underlying theory. At a given scale, the parton distributions can be measured in deeply inelastic lepton
hadron scattering. The evolution of these distributions to larger momentum scales is then prescribed by standard
methods of perturbative quantum chromodynamics. Three things are done in this section. First, we give a
brief summary of the basic ideas of the QCD-improved parton model. We then turn to the task of constructing parton distributions which are appropriate to the very
large momentum scales of interest for a multi-TeV hadron collider. In the final part of this section, we present
the luminosities for parton-parton collisions and discuss their implications in general terms. These will be used in
the rest of this paper to estimate the rates for particular physics processes.
II ~ PRELIMINARIES
A high-energy proton beam may usefully be regarded as an unseparated, broadband beam of quarks, antiquarks,
and gluons. For the hard-scattering phenomena that are the principal interest of this paper, it is the rate' of encounters among energetic constituents that determines interaction rates. We adopt the spirit of the parton model in which the cross section for the hadronic reaction
The idealization that the partons carry negligible transverse momentum will be adequate for our purposes. The prototype hadron-hadron reaction is depicted in
Fig. 1. The general ideas of the parton model are
a +b —+c+ anything
is given schematically by
(2. 1)
do(a +b~c +X)= g f 'fj 'd&(i +j ~c+X'),
partons
(2.2)
where f ' is the probability of finding constituent i in
hadron a, and &fj+j~c+X') is the cross section for the
elementary process leading to the desired final state. This
picture of hard collisions is not only highly suggestive, it also in many circumstances provides a reliable estimate of
ab
FIG. 1. Parton-model representation of a hadron-hadron reaction.
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Eichten et al. : Supercollider physics
thoroughly explained in Feynman (1972). Many interesting applications of the parton model philosophy to hadronic interactions were introduced by Berman, Bjorken, and Kogut (1971). The cross section for reaction (2.1) is given by
S =XgXyS
g —cosO
t=M, —x,xzs 2 smO (2.15)
der(a +b ~c+X)= gf (x, )fJ (xb )d&(i +j ~c+X'), Q =M~ —xbxys 7+cosO
2 sinO
s= sv (2.6)
(2.5) Here
where f;"(x) is the, number distribution of partons of
species i. The summation runs over all contributing par
ton configurations. If we denote the invariant mass of the
i-j system as
2x~s —xgs 7+cosO
sinO
g —cosO
2k+xgxys sinO (2.16)
p =xvs /2, (2.7)
then the kinematic variables x, b of the elementary pro
cess are related to those of the hadronic process by
and its longitudinal momentum in the hadron-hadron c.m. by
Xmin =
++cosO
26+x ps slnO
g —cosO
2s —xmas sinO
(2. 17)
x,,b= ', [(x +4~—)'i+x] . (2.8)
These parton momentum fractions satisfy the obvious requirements
1/2
4M, sin O
X= 1+ XjS (2.18)
ix) =7
Xg —Xb =X (2.10) 5=—Md —M, .
2 2 (2.19)
We shall present detailed cross-section formulas in the text, in connection with the discussion of specific phe
nomena. However, one situation —two-body parton scattering occurs so frequently that it is appropriate to develop the kinematics here. We consider the generic process
a+b~c+d+ anything, (2.11)
py =xiV$ /2, (2.12)
where the masses of the final-state particles are M, and
M~. Then if particle c is produced at c.m. angle 0 with transverse momentum
f
+ (x ) f(o)(x Q2) (2.20)
There is some ambiguity surrounding the choice of scale Q in a particular process. It should be of the order of the subenergy,
The elementary parton model as sketched here is, at best, an approximation to reality. For our purposes, the most important modification to the elementary picture is due to the strong interaction (QCD) corrections to the parton distributions. In leading logarithmic approximation (Czribov and Lipatov, 1972a, 1972b) these corrections are process independent and can be incorporated by the replacement
the invariant cross section for reaction (2.11) is Q =s, (2.21)
E yr
do. 1
d p 7T ~ ~ min
dxg
X+cosO
Xg —Xy 2 sinU
Xx,xbf; '(x, )fj' '(xb) (s,t, u) .
dt
(2. 13)
(2. 14)
The kinematic invariants of the elementary reaction
i +j~c+d
are given by
but the choice affects event rates, and the particular value
of Q used for each process will be stated in the relevant section below. We shall consistently adopt the Born approximation to the elementary cross section and neglect higher-order strong interaction corrections. Experience in specific cases (Altarelli, Ellis, and Martinelli, 1978; Ellis et al.,
1980) shows that the resulting estimates of cross sections should be reliable within a factor of about 2. We also ignore "higher-twist" or hadronic wave function effects. These will produce corrections to the calculated rates
which are proportional to (M /Q )", d & 1, where M is a
scale characteristic of hadronic binding. The effects should therefore be negligible for the processes we discuss.
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Eichten et aI.: Supercollider physics
B. Q2-dependent parton distributions
and
Q ~M (2.22)
x~M /s. (2.23)
In order to predict production cross sections in a hadron collider, we require parton distributions as functions
of the Bjorken scaling variable x and Q . For the study
of a process with characteristic mass M, the parton distributions must be known for
up quarks: u„(x,g )+u, (x,gz),
down quarks: d„(x,Q )+d, (x,gz),
up antiquarks: u, (x, g ),
down antiquarks: d, (x,Q ),
strange, charm, bottom, and top''
quarks and antiquarks: q, (x, Q ),
gluons: 6 (x, Q ) .
(2.28)
The typical momentum fraction contributing to such a process will be
x=M/vs . (2.24)
Since we shall be concerned with characteristic masses in the range
10 Gev/c &M &10 TeV/c (2.25)
and c.m. energies between 10 and 100 TeV, the range of interest for the kinematic variables is
The flavor quantum numbers of the proton are carried by the valence quarks. Those distributions must therefore satisfy the number sum rules
f
dx u„(x,g')=2, (2.29)
f
dxd„(x, g2)=1 .
1he parton distributions are also constrained by the momentum sum rule
1dx x[u„+d„+6+2(u, + d, +s, +c, +b, +t, )]= 1 .
100 GeV' & Q z & 10' Gev' (2.26) (2.30)
and
x &10 (2.27)
Although the distributions have not been measured at
such enormous values of Q, it is in principle quite
straightforward to obtain them. Existing data from deeply inelastic scattering can be used to fix the parton distributions at some reference value of Q =Qo over most of
the x range. Evolution to Q ~QO is then predicted
(Georgi and Politzer, 1974; Gross and Wilczek, 1974) by
@CD in the form of the Altarelli-Parisi (1977) equations. The resulting distributions can be checked against cross sections measured at the CERN SOS Collider and later
at the Fermilab Tevatron. Rather than utilizing any of the parametrizations of parton distributions that appear in the literature, we have developed our own set in order to ensure reasonable behavior over the full range of variables given by (2.26)
and (2.27). It is convenient to parametrize the distributions in a valence plus sea plus gluon form. The proton contains
To improve numerical convergence in the neighborhood
of x =0, it is convenient to recast the familiar AltarelliParisi equations as integro-differential equations for x times the parton distributions. The valence, or "nonsing
let, " distributions satisfy
where
and
p(x, Q )=xu„(x,Q ) or xd„(x,gz)
y =x/z .
(2.32)
The evolution of the gluon momentum distribution
g(x, Q )=x6(x,gz)
is given by
(2.33)
dp(x, Q ) 2s(Q ) ' (1+z )p(y, Q ) —2p(x, Q2)
-d
d ingz 3m. 1 —z
Q 2 1 41n(1 —x) ( Q2) (2 31)
dg(»g ) ~ Q ) f ' 3[zg(y, Q') g(x, Q')]— 3(1—z)(1+z')g(y, g')
d lnQ2 1 —z Z
2 1+ 1-z'
+'3 +, g y[n(y Q')+2e, (y, g')]
Aavors q
+3 ln(1 —x) g (x,Q 2), (2.34)
where Nf is the' number of flavors participating in the evolution at g .
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586 Eichten et al. : Supercollider physics
The evolution of the momentum distributions of the light sea quarks
l(x, Q )=xu, (x,g ) or xd, (x, g ) or xs, (x,g )
is described by
dl(x Q ) 2cts Q 1'' (1+z )l(y g ) —2l(x g )
(2.35)
~,(g') [1+—,ln(1 —x)]l(x, g ) . (2.36)
For the evolution of the momentum distributions of heavy sea quarks
h(x, Q )=xc,(x, Q ) or xb, (x, Q ) or xt, (x,Q ),
we adopt the prescription of Gluck, Hoffman, and Reya (1982),
dh(x, g2) 2a, (g ) ' (1+z )h(y, g ) —2h(x, g )
dz
d lnQ 1 —z
(2.37)
——z(l —z)+
3 1 Mq (3 —4z)z
4 2 g' 1 —z
16M z g(y, g')
3Mq 4Mqz 2Q2 Q2
z (1 —3z)+ ln g(y, g ) 8(p )
1+ 2
1 —P
a, (g )
+ [1+in(1 —x)]h (x,g ), (2.38)
where Mq is the heavy quark mass,
g( ) Oy x (0
1, x)0, (2.39)
and
P= [1—4Mq/Q (1 —z)]'~ (2.40)
The running coupling constant of the strong interac
tions a, (g ) may be expressed in terms of the QCD scale
parameter A as
33 —2'
1/ag(g )—= ln(Q ./A2) .
12' (2.41)
A prescription is required for the variation of &f and
a, (g ) as a threshold is crossed. Since the value of A we
shall adopt has been determined for N~ =4, it, will be consistent to write
1/a, (g )= ln(g /A )
12m
1 8(g —16M; )ln(Q /16M; ) .
i =b, t, . . .
Q.42)
This form ensures a smooth crossing of thresholds and is equivalent to other prescriptions in common use, modulo higher-order QCD corrections which we ignore. As Q
approaches infinity, the contributions of all quarks become equal.
The procedure we follow is to begin with input distri
butions inferred from experiment at Qc ——5 GeV and to
integrate the evolution equations (2.31), (2.34), (2.36), and
(2.38) numerically. The advantage of this over the moment method which is often employed is that for each value of x we require input information only for larger values of x, and not over the full range from 0 to 1. This is important in practice, because structure functions are
poorly known at small values of x. In evolving the distri
butions to larger values of Q we ignore all higher-twist
effects. Our neglect of higher-twist effects is justified by the fact that the starting distributions were derived from
data with (Q ) =5 —50 GeV~. We omit higher-order
QCD corrections (for which see Buras, 1980). These higher-order corrections, which are suppressed by- one
power of a„contain terms proportional to ln(1 —x) and
ln(x). These terms destroy the validity of QCD perturba
tion theory at large and small x. In the large-x region techniques are available to resume the terms of the form
a, ln (1 —x) for all 1 effectively a, (g ) is replaced
by a, [g (1 —x)] (Amati et al., 1980; Peterman, 1980).
Since the structure functions are very small in this region, this change does not affect our results significantly. The situation at small x has been considered by Czribov, Levin, and Ryskin (1983) and recently by Collins (1984).
Higher-order corrections appear to be small at x &10 over the Q range we consider. Any remaining uncertain
ty of course does not affect our estimates of the discovery
limits for various processes, which depend only on
x ~0.1.
Rev. Mod. Phys. , Vot. 56, No. 4, October 1984


Eichten et ai.: Supercollider physics
We must next discuss the input distributions. At the present time, the data of the CERN-DortmundHeidelberg-Saclay (CDHS) neutrino experiment at CERN (Abramowicz et aI., 1982,1983) have the greatest statistical power. We shall therefore take the CDHS structure functions as a reasonable starting point. Some of the experimental uncertainties will be addressed below. Neutrino data are particularly useful, because measurement of the structure function xW3 from an isoscalar target determines the valence distributions as
0. 7
Q. S
o
~5 —X
X 0.4
2= 1 do(vX~p X)
G)ME 1 (1 y)2 dx dy X 0.3
0
da(vN~p, +X) dx dp
=x[u„(x,Q )+d„(x,g )], (2.43)
where Gz is the Fermi constant, M is the nucleon mass,
E is the neutrino beam energy, and the Bjorken scaling variables are defined by t l l
0 O, i 0.2 0.3 0.4 0.6 0. 8 0. 7 0, 8 0.9 1
y =v/E,
(2.44)
(2.45)
X
F1G. 2. Ratio (dotted-dashed line) of valence distributions of up and down quarks (after Eisele, 1982). The dashed line is the result of the parton distributions given by (2.55).
where v =E —E& is the inelasticity parameter. The
CDHS measurements give
xW3(x, go) =1.66x (1—x) '(1+5.86x), (2 46)
for x &0.03 and Qo ——5 GeV . The normalization has
been fixed by continuing to x =0 and enforcing the baryon number sum rule. A lowest-order QCD fit used to evolve the parametrization (downward) to Q =Qo yield
ed the leading-order scale parameter
A=275+80 MeV . (2.47)
The up- and down-quark valence distributions can be separated using charge-current cross sections for hydrogen and deuterium targets. Data from the CDHS and the Big European Bubble Chamber (BEBC) (Bosetti et al.,
1982) experiments are shown in Fig. 2, which suggests the parametrization (Eisele, 1982)
d„(x)/u„(x) =0.57(1—x) . (2.48)
The data are insufficient to exhibit any Q dependence,
and are consistent with the SLAC-MIT electron scattering measurements (Bodek et al., 1979). The simplest
guess that d„.(x)/u„(x) = —, is not in agreement with the data. Once the valence distributions are known, the sea distributions may be determined from measurements of the structure function W2 on isoscalar targets. Data on the flavor dependence of the sea are rather sparse. In principle, the ratio u, (x)/d, (x) can be extracted from neutrino data; it is consistent with unity (Eisele, 1982). The strange sea can be measured directly in antineutrino
induced dimuon production. The shape of s, (x) is shown
in Fig. 3 to be consistent with the shape of u, (x)+d, (x)
determined from P2. The CDHS parametrizations we use are derived using
2s, (x)/[u, (x)+d, (x)]=0.43
at Q =5GeV.
Bounds on the rate of same-sign dimuon production in neutrino-nucleon collisions (Abramowicz et al., 1982,
1983; Eisele, 1982) limit the charmed, sea:
11
f
dxxc, (x) & —' , f dxxs, (x) . (2.50)
We shall assume that at Q =5 GeV the sea distributions
of charmed and heavier quarks can be neglected. Once the quark distributions have been determined, the
integral dxxG(x) of the gluon momentum distribu
0
tion can be determined from the momentum sum rule.
The shape of G(x) cannot be measured directly in electroweak interactions, but a constraint on the shape can be
inferred as follows. With increasing Q, QCD evolution
causes gluons with momentum fraction x & to generate antiquarks with momentum fraction xo&x~. A failure to
find antiquarks at values of x larger than some value xo
thus constrains G(x, go). There is of course a strong
correlation between G(x, g ) and the QCD scale parame
ter A. The larger A is, the more rapidly G(x, g ) will
steepen, and the broader the input distribution G(x, go)
can be. Ideally one would determine A from the evolu
tion of the nonsinglet structure function and then extract
G (x, Q2) from singlet structure functions. The existing data do not permit this to be done unambiguously.
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984


588 Eichten et al. : Supercollider physics
0.10 )Q(
'b,
CDHS x HPWFOR
(v) = 50 GeV
@+5 w p+c
x (G+d+2C ) including slo~ rescaling
o.5 —t
0.4
tl. 3
r
C&
0.2
+ CDHSvN ~ SLAC e-d o CHlO pp o 5LAC e-p
+
EMCEE,
p
001
gal
)h Il
0.1 -,
Ik
0,.
-0.1 0;1
II
0.2 0.3
0I.5
'& j~ ~II h
dE Jt
II I
O.6 0.7 O.s
0.001
FIG. 4. The ratio R =aL/o. T as a function of x for the CDHS neutrino data (Abramowicz et al. , 1983), compared with measurements in ep and ed scattering (Bodek et al. , 1979) and pN
scattering (Gordon et al. , 1979; Aubert et al. , 1983a). The
curve is the QCD prediction for the kinematic range of the CDHS experiment.
iiii Ii
0.1 0.2 0.3 0.0 0.5 0.6 0.7 Xvis
FIG. 3. Comparison of the shape of the strange quark distribution determined in opposite-sign dimuon events (data points) with the antiquark distribution (solid line) deduced from u& (after Eisele, '1982).
A=180+20 MeV (2.54)
and Qo=5 GeV . In Fig. 5 we show the quantities
q„(x,gp), xG(x, go), and x [u, (x, gp)+d„(x, gp)] deter
mined from (2.49) and (2.51)—(2.53). We shall use the following parametrization which reproduces these distributions:
It is therefore necessary to use the singlet structure functions Mq(x, g ) together with the antiquark distribu
tions q, (x,g ) to make a simultaneous fit to A and
G(x, Q ). The difficult-to-measure ratio R =aL, /o. T
enters the analysis. The available data, summarized in Fig. 4, do not determine R precisely. Two fits have been presented to the CDHS data.
Under the assumption that R =0.1, Abramowicz et al. (1983) determine the combination
2.4 -$
Set
qv(»go) =—x [us(»go)+d (»Qo)+2s, (x~go)]
=0.52(1 —x) ' (2.51) 1.2
=(1.1+4.07x)(1—x) ' (2.52)
M2(x, gp) =x Iu„(x,gp)+d„(x, gp)
+2[u (x, gp)+d (x,gp)+s (x,gp)]I
O. S
'.l
0.4
l
0 0, 1 0.2 0.3 0.4 0.6 0.8 0. 7 0.'8 0.9 1
with
xG(x~go) =(2 62+9 17x)(1—x)5'9p, (2.53) FIG. 5. Parton distributions of Set 1 at Q~=5 GeV2: valence
quark distribution x[u„(x)+d„(x)] (dotted-dashed line}, xG(x) (dashed line), and q„(x) (dotted line).
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 589
xu„(x, Qo ) = 1.78x (1 —x ' ')
xd„(x,go)=0. 67x (1—x' ') '
xu, (x,Qo ) =xd, (x,Qo ) =0.182(1—x)
xs, (x,go) =0.081(1—x)s 54,
xG(x, Qo ) =(2.62+9. 1'7x)(1 —x)s 9o,
A=200 MeV .
(2.55)
q„(x,Qo ) =0.53(1—x) ' (2.56)
W2(x~go ) = ( 1.18+3.859x)( 1 —x) (2.57)
and
with
xG (x, Qo ) = (1.75+ 15.575x)(1 —x) (2.58)
A=290+30 MeV (2.59)
and Qo ——5 GeV . The resulting valence quark and gluon
distributions and the combination q„(x,go) are shown in
Fig. 6. Notice that the larger value of A is correlated with a harder gluon distribution at Qo, i.e., one with more
gluons at large values of x. These are reproduced by the following parametrization (Set 2):
The d„/u„ratio implied by this set is consistent with the
measurements collected in Fig. 2. We shall refer to this parametrization as Set 1.
Under the assumption that R =o I /o T has the
behavior prescribed by QCD, Abramowicz et al. (1983) flind
xus(x~go) =xds(»go) =0 185(1—x) '
xs, (x,go) =0.0795(1—x) '
xG (x, Qo) =(1.75+ 15.575x)(1 —x)s.os,
A=290 MeV,
(2.60)
4. 5
Set 1
with the valence distributions xuU(x, Qo) and xdz(x, go)
given in (2.55). It is appropriate to compare our two input distributions with other determinations of parton distribution functions. In Figs. 7 and 8 we compare our parametrizations .with the determinations of the valence, sea, 'and gluon distributions presented by the CHARM neutrino experiment
at CERN (Bergsma et al., 1983) at Q = 10 and 50 GeV .
The agreement of the valence and gluon distributions is satisfactory, but the disagreement seen in the sea distribution is striking. We remark that whereas our distributions satisfy the momentum sum rule to better than 1%, momentum conservation was not explicitly enforced in the CHARM Collaboration fits. There are two other indications that the CDHS analysis might somewhat underestimate the sea quark distributions. The ratio of deeply inelastic lepton scattering on neutron and proton targets has been measured by the SLAC-MIT Collaboration (Bodek et al., 1979) and by the
European Muon Collaboration (Aubert et al., 1983b).
Their data are compared in Fig. 9 with the prediction of
our Set 2 at Q =10 GeV . The prediction does not de
pend appreciably upon Q and is similar for Set 1. The
Set 2
2.4
2. 6
i.6
1.2
0.8 0.5
.I
0. 4
I 0 0. 2 0, 2 0.3 0.4 0.6 0.8 0. 7 0.8 0, 9 1
I . I~ ~ . I-. I
0 O, f 0.2 0.3 0 4 0.6 0.6 0.7 0.8 0.9 1
X
FIG. 6. Parton distributions of Set 2 at Q =5 GeV2: valence
quark distribution x[u„(x)+d„(x)] (dotted-dashed line), xG(x) (dashed line), and q (x) (dotted line).
Flax. 7. Comparison of the gluon distribution xG(x, Q2) (dashed line), the valence quark distribution x[u„(x,g )+d„(x,g )] (dotted-dashed line), and the sea quark
distribution 2x[u, (x, Q )+d, (x, Q')+s, (x, g2)+c, (x, g )] (dot
ted line) of Set 1 with the determination (shaded bands) of
Bergsma et al.— (1983) at go=10 CxeV~.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


59P
4. 5
Eichten et a/. : UPercollider ph gjsics
3.5
2. 5
1.5
o. 5
j
0
J
0, 1 p 2
' ' . -- L~ l
0.3 -4 0 ~ 6
+
0.7 p
It can be seen tha rapi1dly established at
that flavor S
s e heavier fla
ut that ma
vors even a =10 eV =100
:c . ,:, : . : .360.33:0
ions of the p structure
structure f
sequence, we ma
re at small value
that region T
h
a o not exte
o be rnor e specific,
001 01
erefore have
Fits to s
b b d on pau' b
that the m
0 SU po
momentum i
amp e, the r
finite means
q'
g
) t be 1ess singular than
b =5 5 GeVy 2
7
et 2at
fact that
50 Qe+2
at the curve approaches unit e ata do su
ni y at small x 1ess rapid
p
'on. A secon
ee or an enh anced sea
Cl hC b comes from
ggestion that a
1 ' -Fermilab-Roch
the data of the
-F ' - oc ester-Rockef 1
e e ler neu
FIQ 8
X
0, 9
~ . Same comp»arr'»onasFig 7 f
I 30 Ge+y 2
1.0— e LILAC-MIT
~ EMC
trinO ex
Th
urements.
at small x than 1
calculated
an in the
shown f f xG( 2
"pected g~o~th f et 1 in Figs. 10 ~ ) and
deduced fro F or compo 't s own in
he flav . et 2 are
xsg (x Q2)
g 14—17 wh. h
the sea can b i s.
si ion of
xc,(x,g& ' ic show th
~eincl d ' ' x s(x g') d
'evoi«ion of
u e only the, an xr (x
quark sea f e perturbatjv ' . ' ) for Set 2
«m the
e evolution
Perturbattv . process g~ g — of the heav
ol
, and ne le
vy
sky et al
nslc, component
g ect the non
198 ' 980,1981). E " proposed b
ication for a . ' have not giv
~j
ponent. I . . mportant ' . " any posi
n denv1n
1ntrinsic c
have used
g the heavy
charm corn
Iuark distri'b uiions ~e
tC
I 1111 I I I I I Ills I I I I Ill li
0.5— 10
X
x 10
00 I
0.2
0I4 0.6 0.8
FKy. 9. x de
X
dependence o~ sections for dee
s ' r eeply inelasti ng on n
ee ic scattering
th to d' e data are
e solid
(1983b).
from Bodek et al. (1979)
=10
and Auberrt et al.
1
I I I III I I I I I III I I I IIIII I I I I I I I I IIIII
10
FIG. 10. ev ' o
evolution of h
Q' (GeV*)
e gluon diissttrriibbution xG(x
(dotted line) 10 e
d ne, (dotted
Rev. Mod. Ph s, o. 4
Ys., Voi. 56, No. 4, October 1984


Eichten et af.: Supercollider physics 591
10 Ml tlf] I I I I I III( I I I I I I II) I 1 I I I III) I I t I Ill lt I I I I I III[ I I I I I III) I I I I I tll 10 pffft/ I I I 1 I I II' I I I 1 IIII] I I I I I
flies I I I I litt) I I I I lltl( I I I I 1 llf) I I I I fill
(3
X
X 10
1
X
X
—1
10
IIIIII 1 I I l IIIII I 1 I lttttl 1 I 1 fftttl 1 1 1 lttttl 1 '1 I lttttl 1 I 1 1 ltll! I 1 1 1 till
10 10 10 10 10 10 10 10
4 5 6 7' 8
Q' (GeV')
Flax. 11. Q evolution of the up antiquark distribution
xu, (x, g ) of Set 1. The down antiquark distribution xd, (x, g )
is equal. Same values of x as Fig. 10.
I/x at x =0.
To explore the uncertainties in the small-x region we consider two modifications to the gluon distribution of Set 1, as follows:
xG(x, Qll) =(2.62+9.17x)(1—x)5', x & 0.01, (2.62)
2 0.444x-f/2 —1.886 (a)
xG(x, Qft) = 25 56 fn (b)
25. 56x
(2.63)
These modifications match continuously at x =0.01 and are constrained to change the gluon momentum integral by no more than 10%, we demand that
dx xG(x, Qft) =0~.55+0~.05 ~.
0
The results of these changes are presented in Figs. 18—2—02,
which show the Q variation of xG(x, Q ) at x =10
10, and 10 for Set 1, modification (a), and modifica
I lllfl 1 1 I 1 ttftl 1 I I ttttti I t 1 1 ttttl 1 I I lllllI I I 1 t ttttl 1 1 111111I 1 I 1 lltll
10 10 10 10 10 . 10 10
5678 CP (GeV')
FIG. 13. Q evolution of the up antiquark distribution
xu, (x, Q ) of Set 2. Same x values as Fig. 10.
tion (b), respectively. The drastic differences built into the distributions at low Q diminish rapidly as Q rises.
At Q =Qft ——5 GeV, the values of xG(x, Q ) given by
modifications (a) and (b) differ by a factor of. 160 at
x = 10 . After evolution to Q = 10 GeV, quite a
modest value on the supercollider scale, this difference is diminished to a factor of 2. We regard this example as extremely reassuring, for-it implies that the gluon distribution at small x and large Q may be much better determined than is commonly believed. Another source of uncertainty is variation of the QCD
scale parameter A. To study this effect we have evolved
the starting distributions of Set 1 with A=100 MeV. The results are shown in Fig. 21 for xG(x, Q ) and in Fig. 22
for xu, (x, Q ). Comparing these with the plots of Figs.
10 and ll, we find that over the range Q =10 —10
GeV the effect of this charge is to alter the distributions
by no more than 20%. The input structure functions we use have been derived principally from neutrino scattering from heavy nuclei under the assumption that these are related additively to proton and neutron structure functions. Recent data (Au
I tiffs I I I I I III'
Set 2
I 1 I I lilt[ 1 I 1 I IIII' I I I I IIII[ I I I f 1 lit( I 1 I 1 tlffi I I I I I III 10 &I III) I I I I I III[ I I I I IIII( I I I I 1 III) I I I I IIII[ I 1 I I IIII( I I I I I III) I I I I fill.
10 8
C3 X
10
X
NX
—1
10
1
I I IIII I 1 I I ltlll I I I IIIIII 1
10 10 10
I I 1 tttII 1 1 I tttttI 1 I I IIIIII I 1 I
10 10 10 10 10
I 1 tttI I I I I tlttI 1 I I I IIIII I I I I IIIII 1 I I I IIIII I 1 I I 1 IIII I I I I!ttfl I I 1 I litt
3 4 '5 e 7 8
10 10 10 10 10 10 10 10
FICr. 12. Q evolution of the gluon distribution
Set 2. Same x values as Fig. 10.
(GeV )
xG(x, g ) of
I (GeV')
FICx. 14. g evolution of the strange quark distribution
xs, (x, Q ) of Set 2. Same x values as Fig. 10.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et a/. : Supercollider physics
bert et al., 1983c; Bodek et al., 1983a,1983b; Cooper et al.,
1984; Asratyan et al., 1983; Arnold et al., 1984) indicate that this is not the case. Representative measurements are shown in Fig. 23. It is generally agreed that the ratio
Fq'/F2 of the structure function per nucleon (extracted
neglecting nuclear effects) is 10—15%%uo below unity at
x=0.6. This behavior cannot be explained by Fermi motion (Bodek and Ritchie, 1981) within the nucleus. At small values of x the experimental situation is confused. The European Muon Collaboration data (Aubert et aL, 1983c) show a significant enhancement of the iron structure function at x &0. 1, but this is not confirmed by the
SLAC data of Arnold et al. (1983) at somewhat smaller
values of Q . These observations suggest that the valence distributions we have used may be about 10%%uo too small
in the neighborhood of x =0.6 and that the sea distribu
tions could be as much as 15%%uo too large at x =0.1. Given the earlier hints that the sea distributions may be slightly too small, we do not regard this as a serious problem. Better data at larger values of Q would again be
helpful, as would a theoretical understanding of the nuclear phenomenon. The effect of the nuclear environment on G (x, Qo) and A is not known. We conclude this discussion with a brief comment on other parametrizations of parton distributions (Gluck, Hoffmann, and Reya, 1982; Baier, Engels, and Petersson, 1979; Owens and Reya, 1978; Duke and Owens, 1984). The standard practice has been to evolve input distributions at Qo over a range in Q and to fit the resulting dis
tributions to analytic forms in x and Q . Most of these
fits have been available for several years and entail values of the scale parameter A of order 400 MeV, somewhat larger than the current best fits. For comparison with the input distributions we have used, which are shown in
Figs. 5 and 6, we plot in Figs. 24 —27 the parton distribu
tions at Q = 5 GeV of Baier, Engels, and Petersson
(1979), and of Gluck, Hoffmann, and Reya (1982), both
with A=400 MeV, and both the "hard-gluon" (A=400
MeV) and "soft-gluon" (A=200 MeV) distributions of Duke and Owens (1984). The distributions which involve
the large value of A=400 MeV have harder gluon distri- ' butions than do our parametrizations, as expected. We do not display the Owens-Reya (1978) distributions, because
the low value of QII — —1.8 GeV used there invites distor
tions due to higher-twist effects, and because they are superseded by the work of Duke and Owens (1984). The distributions of Baier et al. (1979) and of Duke and Owens (1984) have SU(3)-symmetric sea distributions and do not include heavy flavors. In addition, Baier and collaborators (1979) have fixed u„(x,Q )=2d„(x,Q ) at all
values of x and Q .
The Q evolution of these fits is shown in Figs. 28 —31,
where we display the gluon momentum distribution xG(x, Q ). Figure 28 shows that the parametrization of
10 &I III[ I I I I I ill[ I I I I IIII[ I I I I I III[ I I I I till[
Set 2
I I I I I ill[ I I I I I Ill[ I I I I till
1
X
OX
—1
10
Baier et al. (1979) is unreliable for Q & 10 GeV, where
xG(x =0.1,Q ) begins to increase with Q . The
parametrization of Gluck et al. (1982) is correctly
claimed (see Fig. 29) to be sensible for x &0.01 and
Q &4)&10 GeV . Notice, however, the odd behavior at
small values of x that results from blind extrapolation of their fit. Moreover, this parametrization deviates by as much as 20% from the exact result obtained by evolution even within the claimed domain of validity. Figure 30 shows that the "hard-gluon" parametrization of Duke and Owens (1984) cannot be trusted for Q &10 GeV2. Their soft-gluon parametrization behaves reasonably all
the way to Q = 10 GeV, as shown in Fig. 31. Compar
ison with Figs. 10 and 12 shows that our distributions
contain fewer gluons at small x and large Q than did these earlier parametrizations.
Q. Partpn-parton luminpsities
In the succeeding sections of this paper we shall use the
parton distributions derived in Sec. II.B to compute differential and total cross sections for many reactions of po
10 &lilt[ I I I I IIII[ I I I I I IIII I I I I IIII[ I I I I I I III I I 111111[
Set 2
I I I I till[ I I 11114l
nO X
X
—1
10
10-2 I I I III I I I I I I III[ I I I I I II II I I I I I I III I I I I I III[ I I I I I I III I I I I I IIII I I I I I I I I
10 10 10 10 10 10 10 10 Q' (Gev')
FICs. 15. Q evolution of the charmed quark distribution
xc, (x, Q ) of Set 2. Same x values as Fig. 10.
10-2 I
I I IIII I I I I I IIII I I I I I IIII I I I nfl tll I I I I I I III I I I I IIII[ I I I I I I III t I I I I Ill
10 10 10 10 10 10 10 10
For a review and a list of theoretical references, see Llewellyn Smith (1983).
FIG. 16. Q evolution of the bottom quark distribution
xb, (x,Q2) of Set 2. Same x values as Fig. 10.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eiehtgn 'g8g~ Bl. SUpgrcotlid~r
10 IIIII I I
II I I IIIII I I I I I I III
Set 2 290 MeV
I I I IIIII I I I I I IIII I I I I I lll i0 I I I I I I I. I M I I I
0
X
X
10
X 10
X
10 10 10 105 106 10 10
FIG. 17
CP (Gev')
Q evolution of the to nark
ofSt2. S 1
e x va ues as Fig 10
Set & (a)
200 MeV
I I I II I I I I
10 10
10
FIG. 19.
Q' (Gev')
Q evolution of the gluon dis
e g uon d st ibution funct on )(
tential interest at t."..e supercollider. Such detailed
of ues tioone d val1ue for det
consi eration of the ph sics Ho h b 1
b t, 1
can e earned about the ener , energy, an luminosit b
g yy p g
m = s, the c.m. energy of the collidin arto
convenient quantity is the d'ff
is e j. erential luminosity
dW r ' ()
f
d [f~(ci( )f~(b~(,/ )
+f1"(x)f '(~/x) J/x,
where, ~' '(x) is the num. ber distribution of
o11'd
'ng momentum fraction x
co i ing with c.m. ener
bl' " "'"b
'ven y
~=ttI2/s =s/s .
(2.65)
(2.66)
interval (r, ~+d~ per hadron-hadron calli '
' f m ' o 'o fo
ss section or the hadronic reaction
a +b —+a+ anything
is given by
dQ dW"
(ah ~aX)=
7 o ij~a),
gJ
(2.67)
(2.68)
(T(s) =c/s . (2.69)
where &(i ~a
j
is the cross section for t op t e
xp icit forms of &
h""n'his ' " '0
The interesting hard-scatterin ro
g pmcesses that defi
p ysics motivation of a m
have a commonn asymptotic form r
a multi-TeV collider
sional analysis
prescribed by dimen
The differen '
ential lummosity represents the n
parton-parton collisi h ca . . ' ' e
isions witn sca»
isi n cal " c.m. energies in the
For a stron g--'interaction process, such as 'e p p odllc
o or er (a, /~) . F
tm k as lepton pair productio' n, ersap
10 I I I I I I I I 10 I I I I I I I I I I I I I I I
0 10
X VX
X 10 X
Set 1
h. = 200 Mev
10
I I I I I III
8
I I I I I I II
10 Q2 10
FIG. 18.
(GeV')
Q evolution of thee gluuoonn distribution function
10 (dotted-dashed line).
Set ( (b)
A 200 Mev
I I I I I I II
10,
I I I I I I II
10
FEG. 20. ev
Q~ (GeV )
G(,Q ) of S 1(b) fo ), 10 (d hd
Rev. Mod. Ph s. V
y ., oi. 56, No. 4, October 1984


594 Eichten et al. : Supercollider physics
2
10
73 X
10
X
I I 1 Ill I ! I I ll'II) I I I I I l Ill I I I I 1llll
Set
h, = 100 MeV
I I I I lull I I I I lull I I I I I!Ill I I I I I III
t
IO
t 0.9
0.8
I I l ~1 1 1 l I I 1 1 l 1 1 1 I
Fe ~ 0 -21 5
~
Arnold
P' Q v
+t
j 4 „Q
y ~IW
~ CIVIC
l 1 I I l 11 l 111I 1
0.2 0.6 O.a
11111l - I I I I lllll I I I I IIIII I
10 10 10
I I I IIIII I I I IIIIII I I I I IIIII I I I I lllil I I I I IIII
10 10 10 10 10
g' (Gev')
FIG. 21. Q evolution of the gluon distribution function
xG(x, Q ) of Set 1 with A=100 MeV. Same x values as Fig.
10.
proximately (a/~) . Resonance production cross sections are proportional to w. Consequently, the quantity (~/s)dW/d~, which has dimensions of a cross section, provides a useful measure of the reach of a collider of given energy and hadron-hadron luminosity. In Figs.
32 —50 we plot (r/s)dW/d~ as a function of s, the
square of the parton-parton c.m. energy, for a number of parton combinations in proton-proton collisions at total c.m. energies of 2, 10, 20, 40, 70, and 100 TeV. These luminosities are based upon Set 2 of parton distributions
characterized by A=290 MeV, as specified in Eq. (2.60);
we have taken Q =s. Some additional luminosities are
displayed in Figs. 51—56 for proton-antiproton collisions, where those differ appreciably from their counterparts in proton-proton collisions. The difference between pp and pp collisions is particu
larly pronounced for the uu luminosity, because the antiproton carries valence antiquarks, whereas the proton
does not. The ratio of rdW/d~ for uu interactions in pp
and pp collisions is plotted as a function of the parton
parton c.m. energy w in Fig. 57 for several collider ener
FIG. 23. The ratio of the nucleon structure functions I'2 mea
sured on iron and deuterium as a function of x. Data are from the European Muon Collaboration (Aubert et al. , 1983c) and
SLAC Experiment E-139 (Arnold et aI. , 1983).
2.8 Baler et al.
gies. Roughly speaking, the advantage of pp over pp col
lisions in this channel becomes appreciable for
v ~= w/v s ) 0. 1. Whether this advantage at large
values of v ~ can be exploited depends upon the event rate determined by cross section and luminosity.
Especially useful for judging the effects of changes in luminosity or beam energy are contour plots showing at
each energy vs the parton-parton energy +s corre
sponding to a particular value of (r/s)dW/d~. Some
important cases are displayed in Figs. 58—63 for the par
ton distributions of Set 2, and in Figs. 64—69 for the parton distributions of Set 1.
10 I I I I I I Ill I I I I I l Ill I I I I I I lll I I t I I I ill I I I I I l Ill
Set 1
I I I I I l Ill I I I I I IV. i. e
0'
X
X3
0.8— /
~I
I'.
0.4 —.
Io
I I 1 Ill I I I I I llll I I I I I I Ill I I I I I IIII I I I I I IIII I I I I I I III I
—2 10 10 10 10 10 10 Q2
I I I I I III I I I I I I II
10 10 (GeV )
FIG. 22. Q evolution of the up antiquark distribution
xu, (x, Q ) of Set 1 with A=100 MeV. Same x values as Fig.
10.
I l ~~ t
0 0 ' 1 0. 8. O. S F 4 0 ' 5 0..6 0 ' V 0.8 0.9 1 X
I
FICx. 24. The parton distributions of Baier, Engels, and
Petersson (1979), at Q2=5 GeV: valence quark distribution
x[u„(x)+d„(x)] (dotted-dashed line), xG(x) (dashed line), and
q (x) (dotted line).
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eiehten et a/. : Supercollider physics 595
GHR 8.8 Do(2oo)
2.4 2.4
1.2— 1.2
0.8
0. 4
/
~I'~.
0.8
./ I
~
0.4 —. I
I I ' ~ ~I ~ . . L
0 0, 1 0.2 0.3 0.4 0.6 0. 6 0.7 0. 8 0, 9 1 0 0. 1 0, 2 0.3 0.4 0.5 0.8 0.7 0.8 0. 9 1
FIG. 25. Parton distributions of Gliick, Hoffmann, and Reya
(1982), at Q = 5 OeV2: valence quark distribution
x[u„(x)+d„(x)] (dotted-dashed line), xG(x) (dashed line), and q„(dotted line).
FIG. 27. "Soft-gluon" (A=200 MeV) parton distributions of
Duke and Owens (1984) at Q2=5 GeV: valence quark distribution x[u„(x)+d„(x)] (dotted-dashed line), xG(x) (dashed line), and q (x) (dotted line).
z. e
2. 4
Do(4oo)
The contour plots contain a great deal of information, and will reward a detailed study. Here we call attention to only one particularly general and im ortant feature. Contour lines rise less rapidly than s =const&(Ms, principally because of the 1/s behavior of the hardscattering cross sections. This means in general that to take full advantage of the potential increase in discovery reach afforded by higher collider energies, it is necessary to increase luminosity as well as beam energy. This effect is universal, but is more pronounced for valence-valence interactions than for gluon-gluon interactions.
I IIII} I I I I I III} I I IIIII} I I I IIIII} I I I I IIII} I I I I IIII} I I I I IIII} I I I IIIII
1.2 02
0. 8
0.4 I
Cf X
ex 10
I 1 ~ ~ ~ I. . I
0. 0, 1 0.2 0.3 0.4 0.5 0. 6 0. 7 0. 8 0.8 1
FIG. 26. "Hard-gluon" (A =400 MeV) parton distributions of
Duke and Owens (1984) at Q2=5 GeV2: valence quark distri
bution x[u„(x)+d„(x)] (dotted-dashed line), xG(x) (dashed line), and q„(x) (dotted line).
, »IIII I I I I IIIIl I I I «III}
10 10 10
«»IIII I »I»II}»»«II} «»«»} 10 10 g1S0 i0 10
(GOV')
FICx. 28. Q evolution of the gluon distribution xG(x, Q ) of
Baier, Engels, and Petersson (1979). Same x values as Fig. 10.
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984


Eichten et a/. : Supercollider physics
2
10
I I I lllllj r I lrrrrrj r I I llltlj r I I llllrj r I I rllllj I r 1rlrllj I I r IIIII
GHR
2
10
r I 1 III r r r I I I III I r r rr I II
I
r I I I I 1lrj r l r I I I III I I r I llrlj I 1 I I rr llj r r r I I III
OI X
10
0
X 10
X
rrrlll r r r fllllj r r t Ilrlrj I r r rrrllj r r l frlrlj r r
10 10 10 10 10
r r r rrrrrj r r r rrrrr
10 10 10
1
r rrrlj I l r r lrltj r
10 10 10
r r rrrrrj r r r Ilfrll l I I irrllj I t
10 10 10 10 10 Q' (GeV')
FICi. 29. Q evolution of the gluon distribution xG(x, Q ) of
Gliick, Hoffmann, and Reya (1982). Same x values as Fig. 10.
Q (Gev )
FIG. 31. Q evolution of the "soft-gluon" (A=200 MeV) dis
tribution xG(x, Q2) of Duke and Owens (1984). Same x values as Fig. 10.
III. PHYSICS OF HADRONIC JETS
A. Generalities
This section deals with the production of jets of hadrons that emerge with high momentum transverse to the direction of the incident beams. Experiments at the CERN SppS Collider (Arnison et al., 1983d, 1983e; Bag
naia et al., 1983a) and at the CERN Intersecting Storage Rings (Albrow, 1983) have shown that for an important class of events the jets are well collimated, isolated, and straightforward to analyze. The simple parton-model picture of jet production in QCD was represented in Fig. 1. Constituents (quarks, antiquarks, or gluons) of the incident hadrons appear with momenta distributed according to the parton distribution
functions f '(x„g ) introduced in Sec. II. These con
stituents then scatter at wide angles into outgoing partons which then materialize into the hadrons which are observed experimentally. The details of this hadronization are beyond the scope
of perturbative @CD. However, perturbative methods do suffice (Sterman and Weinberg, 1977; Shizuya and Tye, 1978; Einhorn and Weeks, 1978) to show that distinct jets should exist, and should become increasingly collimated with increasing jet energies. The angle 5(E), which defines the outermost angular distance from the jet axis at which any appreciable hadronic energy is to be found, is
expected to decrease roughly as E ' . There is also a suggestion that at very high energies, gluon jets should be somewhat broader than quark jets, with
5(gluon)=[5(quark)] ~ (3.1)
8
10
10 4
10
In principle, the hadronization could be calculated in complete detail by nonperturbative methods. This is akin to a complete solution of the confinement-problem, for which practical techniques are not yet available. As a
consequence, a variety of models (Ali et al., 1979a,
r Irrrj I 1 l rrrrrj
DO(4O
r r I rrrrrj t r r rrllrj r r I rlrrrj I r I lrrllj r r I rrrrfj r r l rrlrl 3
10
2
10
Cl 10
O X
10
X
I rrirI I r I I IIIII r I r I IrrII r r r I rrrrI I r I r IIIII r r r r IIIII r r I r I IIII r
10 10 10 10 10 10 10 (GeV')
I r I I III
10
1 —1
t
10 10-2 -3
~ 10 10-4
10-5
10-8 10
I I Ill 10
2)
I I I il I I I I I I II
10
vs (Tev)
FICr. 30. Q evolution of the "hard-gluon" (A=400 MeV) dis
tribution xG(x, Q ) of Duke and Owens (1984). Same x values
as Fig. 10.
FICi. 32. The quantity (~/s)dW/d~ for gluon-gluon interactions in proton-proton collisions. Collider energies V s are given in TeV.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 597
6
10 10
5
10 10
4
10 10
3
10 10 2
10
C 10
10
10
D1
10 20 -2
1
'Q
1
10
10
10-3 —3
10
—4
10 10-5
10-4
I IIII I
—5
10
I I I I I I II
I I I I III
10-6 I I I I IIIII 10
I I I I II —1
v'f, {Tev)
10 &I (Tev) 10
FIG. 35. Quantity (r/s)dW/dr for ug interactions in protonproton collisions.
FIG. 33. Quantity (r/s)dW/dr for ug interactions in protonproton collisions.
1979b,1980; Hoyer et aI, 1979; Paige and Protopopescu, 1980; Andersson et al., 1983; Odorico, 1980a,1980b,1983;
Mazzanti and Odorico, 1980; Field and Wolfram, 1983; Gottschalk, 1984; Field, 1983) have been constructed to simulate the evolution of partons into hadrons. Although they differ in detail, all have the common feature that jets become easier to isolate at high energies. This is in agreement with the observation that the jets observed in pp col
lisions at vs =63 GeV (Albrow, 1983) or in e+e col
lisions at v s =7.4 GeV (Hanson et al., 1975) are less dis
tinct than those measured in pp collisions at Vs =540
GeV (Arnison et al., 1983d; Bagnaia et al., 1983a) or in
e+e collisions at Vs =30 GeV (Mess and Wiik, 1983). The perturbative @CD prediction quoted above en
courages the hope that the situation will becoine still simpler at higher energies.
6
10 6
10 5
10 5
10
10
3
10 10 2
10
C 10
10
10
1
10—1
&40 10-2
—1
10
—2
10
—3
10
—3
10 10-4
—5
20
—6
10
—4
20 10-5
I I I I I I III
I ) IIIII I I I I I I I II
10 v's (Tev) 1
I IIII
10 &e (Tev)
—6
10 10
10 10 10
FK". 34. Quantity (r/s )dW/dr for dg interactions in protonproton collisions.
FICx. 36. Quantity (r/s)dW/dr for sg interactions in protonproton collisions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984
Jet studies in hadron-hadron collisions have traditionally been viewed as less incisive than those carried out in electron-positron annihilations or in lepton-nucleon scattering because of the added complexity of events. The SppS experience indicates that, as hoped, the hardscattering events take on a much simpler aspect at high energies, and there is no impediment to detailed analyses. We may therefore expect to take advantage of the higher energies attainable in hadron-hadron collisions and of the
greater diversity of elementary interactions made possible by our unseparated broadband parton beams. What will be the goals of jet studies at supercollider en
ergies? Jets unquestionably will constitute one of the ma
jor sources of conventional background to new discoveries, so it is crucial that they be well understood, if
only for engineering purposes. For exatnple, a thorough


598 Eichten et af.: Supercollider physics
6
10 = I I I I I I I II
5
10 4
10 3
10
I I I I I I II' I I I I I I lg 6
I I I I I I ll(
5
10
10
-10
I I I I I I lit I I I I I I I E
10
10
01
-1
10 2
~ 10 3
10 10-4
10-5
10
I I I I I IIII
10
I I I I I I ill & I
(Tev) 1 10
10
LCl
10
1
—1
10 -2
~1O 10-3
—4
10
—5
10
—6
10 —2
10
I I I I I I ill
10
I I I I I I III
Vs (TeV)
I I I I III
10
FICx. 37. Quantity (r/s)dW/dr for uu interactions in protonproton collisions.
FIG. 38. Quantity (r/s)dW/dr for ud interactions in protonproton collisions.
study of conventional sources of jets will be an important prelude to multijet spectroscopy, which may be an ex
tremely valuable search technique. It may even be possible, in time, to use jets as a parton luminosity monitor, as
Bhabha scattering is used in e+e collisions. The study of hadronization and the investigation of differences be
tween quark jets and gluon jets benefits in an obvious way
from high jet energies and from the possibility of tagging
(or enriching a sample of) quark or gluon jets. Finally,
tests of short-distance behavior such as searches for evi
dence of compositeness, rely on an understanding of the behavior anticipated in QCD.
B. Two-jet final states
The reactions that may occur at lowest order (a, ) in QCD all are two-body to two-body processes leading to final
states consisting of two jets with equal and opposite transverse momenta. The cross section is conveniently written in
terms of the rapidities Vi and V2 of the two jets and their common transverse momentum pi. (Here and throughout this
paper, we neglect the intrinsic transverse momentum carried by the partons. ) It is
/
„p,g[f, "(X,.M')fj'"(», ~')~;,(s, r, u)+ f,"(x.M')f("(x, ,m')&,,(s,u, r )]/(l+S,,),
dV idV zdpi s
6
10 5
10
/4
10
I I I I I I II] I I I I I I lg
r p(«) ==:
6
5
10 4
10
I I I I I lli I I I I I I I g
UU
10 10
10
C 10
1
10
40k -2
h 10 10-3
—4
10
—5
10 10-6 10
I I I I I I ill I I I I I I Ill
10 1
&s (Tev)
I I I ) I I II
10
10
10-3
10
—5
1O
10-6 I I I I I I
10
I I I I I I III
4s (Te&)
I I I I I I II
FICs. 39. Quantity (r/s)dW/dr for dd interactions in protonproton collisions.
FICi. 40. Quantity (r/s)dW/dr for uu interactions in protonproton collisions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 59S
6
10 I I 5
10
10 I I I I I I III I I I I I I I/
I I I I I IP I I I I IIII
5
10 4
llag
I I I I I I III
pp(d@ '==
pp(ds
io 10
10 10
10 CCl 10
10
OC 10
1
-1
'0 10 &0 10-2 -2
~10
10-3
10-4
10-3
10-4
10-5
10-6
10-5
10-6 10
I I I I I I II I I I I I I II
' ~
I I I I I tli
I IIII I I I I
10 (Tev)
I I I I I IIII
10 10 10
~g (Tev)
FICs. 41. Quantity (r/s)dW/dr for ds interactions in protonproton collisions.
FIG. 43. Quantity (r/s)dW/dr for dd interactions in protonproton collisions.
where s =sr is the square of the parton-parton subenergy.
Defining x, =v ~e
(3.6)
x, =v~e '
(3.3)
Finally, the invariants may be expressed in terms of
aQd
cosH =(1 —4p f js )' (3.7)
1
3'boost = T(XI+3'2) ~ (3.4)
we may write
t = ——(1—cosH),
2
4p 2
cosh y*
S (3.5) (3 g)
6'= ——(1+cosH) .
S 2
10
3
10
3
10
2
10 10
ac io
10
C
'0
~+ 10
~10
1
'Q
e 10
4N
10
—3
10
—4
10
10-5
10-3
10
10-5
10-6 I I Ill 10-6
I I I I I I II
I I I I I III I I I I
10 (TeV)
—1
10
10
10 10
10 v'S (Tev)
FIG. 42. Quantity ( /s~)dW/d four uc interactions in protonproton collisions.
FIG. 44. Quantity (r/s )d Z/dr for uu interactions in protonproton collisions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984
the cosine of the scattering angle in the parton-parton
c.m. , as


600 Eichten et af.: Supercollider physics
4
10
3
10
2
10
4
10
3
10
2
10
10
C
1
~ 10
10
10-3
1
'U
10-1
&CO
10
10-'4
—6
10 10-2 10 1
Vs (TeV) 10
10
10 —1 4s {Tev} 10
FIG. 45. Quantity ( /rs )dW/d~ for us interactions in protonproton collisions.
FIG. 47. Quantity (r/s)dW/dr for ss interactions in protonproton collisions.
(3.9)
Quark-antiquark annihilation occurs through gluon exchange in the direct channel, as shown in Fig. 71. The cross section is
The sum in (3.2) runs over all parton species i and j.
The elementary cross sections have been calculated by many authors, and have been summarized by Owens, Reya, and Gliick (1978). There are seven processes of interest; we treat them in turn. The scattering of quarks or antiquarks of different flavors proceeds by t-channel gluon exchange, as shown in Fig. 70. The cross section is
4g A )+
~(aej ~eej ) = 9s t
«s t++u'
cr(VrrIi ~VjrIJ ) = 2 ~ ~+J ~
9s s (3.10)
4Q (~+g 2 2+ 2
~(elan ~@4)= +
9s s
2~ 2 3st
(3.11)
Two-gluon annihilation of a quark-antiquark pair occurs through the s-, t-, and u-channel diagrams pic
The scattering of quarks and antiquarks of the same flavor has both an annihilation component and an exchange component, shown in Fig. 72. The elementary cross section is
10
3
10
2
io
I I I I I I II I I I I I I I I I I I I I I I E
4
10
3
10
2
10
I I I I I llli I I I I I I III I I I I I IIE
10-1
10
JC5
1 O
10 &fll 10-2
10
—4
10
10
—6
10
10 10 1
&s {Tev)
10-4
—5
10
10 10 QQ {Tev) 10
FIG. 46. Quantity (r/s)dW/dr for cs interactions in protonproton collisions.
FIG. 48. Quantity (r/s)dW/dr for cc interactions in protonproton collisions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et aI.: Supercollider physics
4
I I I I I I II[
3
10
2
10
I I I I I Ill I I I I I I IE
pp(bb)
4
10
10
10
I I I I I III I I I I I I II I I I I I I E
10 10
C
1 D
1
10 ff5 10-2
—4
10
10-5
—6
10 —1
10 ~~ (T v) 1 10
1 D 1
10 &0 10-2
10-3
10
10-5
10-2
I I I I I I I Ills
—1 Ws (TeV)
I I I I I I II
10
FICx. 49. Quantity (~/s)dW/d~ for bb interactions in protonproton collisions.
FIG. 51. Quantity (~/s)dW/d~ for uu or uu interactions in proton-antiproton collisions.
tured in Fig. 73. The elementary cross section for this
process is a, (s +u )
@w w)= s
14
t 9 (3.14)
8a, (t +u )
a(a4 3$
41
9tu s (3.12)
The cross section for the inverse process, for which the diagrams are shown in Fig. 74, differs only in the color
average [(—, ) rather than ( —,) ]. It is
3a, (t +u )
@gz e;4) = Ss
4 1 (3.13)
The scattering of a gluon from a quark or antiquark is driven by the s-, t-, and u-channel exchanges shown in Fig. 75. The cross section may be expressed as
Gluon-gluon scattering proceeds by a contact term in addition to gluon exchanges in s-, t-, and u-channels (see Fig. 76). The elementary cross section is
9a, tu su
tr(gg 2s s2 st
uA. 2 (3.15)
Before Eq. (3.2) can be evaluated, we must fix the scale
M appearing in the structure functions and the scale Q2
at which a, (Q ), the running coupling constant of the
strong interactions, is determined. If QCD perturbation
theory is to apply, these scales should be characteristic of
10
10
2
10
I I I I I I Ili I I I I I I I I
i
I I I I I I IK 4
10
3
10
2
10
10 c 10
h1
D
10
CO —2
10
10-3
10—1
&Ol
—2
10
10
10-5
I I I I I —1
10 ~~ (T v) 1 10
10
10-5
—6
10 I I I I III —1
10
I I I I I IIII
(Tev)
I I I. I I III 10
FICi. 50. Quantity (r/s)dW/dr for tt interactions in proton
proton collisions. The t-quark mass is taken to be 30 GeV/e .
FICx. 52. Quantity (~/s)dW/dv for ud or ud interactions in proton-antiproton collisions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


602 Eichten et al. : Supercollider physics
4
10
3
10
2
10
10
3
10
2
10
10
C
1
'0 —1
D ie tN 10-2
—3
10
—.4
10
10-5
10-6 I IIII 10
I I I I I I II
&s (T~V) FIG. 53. Quantity (z/s)dW/dr for dd or dd interactions in proton-antiproton collisions.
1
D
F10
—2
~10
10-3
10-4
10-5
—B
10 I I I I I I II
I I I I I I ill I I
ie 1
4s (Tev)
I I I I I II
Quantity (v/s)dW/dr for ud or ud interactions in proton-antiproton collisions.
the hard-scattering process. Several alternatives [among
them s, t, u, p~, or 2stu/(s +t +u )] suggest them
selves. Different choices, including different values for
M and Q, lead to cross sections which may differ by
20%%uo in the kinematical regime of interest to us. At lowest order in perturbation theory the choice is ambiguous, because, as is well known (Hinchliffe, 1982; Lepage, 1983), any shift in M or Q induces terms in o,j
of order a, and these are being neglected. The O(a, )
corrections to cr;J are known only for the reaction q;qj ~q;qj (Ellis et al., 1980; Sl'ominski, 1981), where they
are large and positive. These corrections are reduced by
the choice of small values of M~ and Q . Having chosen
a scheme in which the a, corrections are relatively small,
one is left to hope that successive terms in the perturbation expansion will be small, so that the Born term at
O(a, ) will give a good approximation to the exact all
orders result. %'e make this choice
M =Q =pf/4 (3.16)
for all high-p~ processes; as a consequence of this reasonable but arbitrary choice, the cross sections we quote will
be uncertain by 20%%uo, even if the parton distributions are known exactly. %"ith these caveats, we now present our results. We first show the one-jet differential cross section do./dptdy ~s o for pp collisions, at c.m. energies of 10,
40, and 100 TeV in Figs. 77 —79. The figures show separately the contributions of gluon-gluon final states (gg~gg and qq~gg„dotted-dashed lines), gluon-quark
( —) ( —)
final states (g q —+g q, dotted lines), and quark-quark fi
4
10
3
10
2
10
4
10
3
10
2
10
c 10 C
1
10
2
~ 10
ie -3
—4
10
10-5
10-B 10
I I IIII I I I I I
10 &e (Tev)
I I I I I I II
10
1
—1
~ 10
10
—3
10
—4
10
10-5
10-B 10
I I IIIII I I »»III
10 1
~~ (TeV)
I I I I I I II
FIG. 54. Quantity (r/s)dW/d~ for uu interactions in protonantiproton collisions.
FIG. 56. Quantity (v/s)dW/dr for dd interactions in protonantiproton collisions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al.: Supercoliider physics 603
4
10 I I I I I I lli I I I I I III
10
I I I I I II
PP(«)
I I I I II
3
10
Io
10
Set 2
I I I I I I lit I Iiill I I I I I I II 1
10 10
FIG. 57. Ratio of (~/s)dW/d~ for uu interactions in pp and
pp collisions, according to the parton distributions of Set 2.
Collider energies i s are given in TeV.
—1
10 I I I I I I I I
10
I I I ! I II
10
(Tev)
FIG. 59. Contours of (~/s)dW/d~ for ud interactions in pp
collisions according to the parton distributions of Set 2. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
( —)( —) ( —)( —)
nal states ( q q ~ q q and gg~qq, dashed lines). In
our calculations we have included six quark flavors, without any threshold suppression. Over the kinematic range of interest, this approximation leads to negligible errors in the rate estimates. At small transverse momentum the two-gluon final state dominates. This is a consequence of the large cross section (3.15) for the reaction gg~gg and the large gluon distribution at small values of
x (cf. Fig. 5). As pi increases, the gluon-quark final state
grows in importance, and at the very largest values of pi
the two-quark final state dominates. At 90, the two
quark regime is essentially unreachable. For an integrated
luminosity of f ddt=10 cm at 40 TeV, we expect
no more than one event per year per GeV/c of pi per unit
of rapidity in this region.
Figure 80 shows the effect of a change in the distribu
tion functions (to Set 1, with A=200 MeV) at Ms =40 TeV. The resultant change is quite small: a 10% decrease
at pi=1 TeV/c. While we cannot be certain that this
represents the widest variation to be expected from changes in the parton distributions, it does give us confidence that reasonable changes in the distributions will not lead to wild variations in the conclusions. Proton-proton and proton-antiproton jet cross sections
at 90 are essentially equal at Vs = 10 TeV, and of course at higher energies. The proton-antiproton cross section is plotted in Fig. 81, to be compared with Fig. 77. For completeness we show in Figs. 82 and 83 the jet cross sections in pp collisions at 540 CieV and 2 TeV. At these low
values of pz the results are slightly more sensitive to the
I I I I I II I I I I I I I I I I I II I I I I I I
io — PP(~U) PP(~O)
0
Set 2 Set 2
—1
10 I I I I I I I I
'10 &s {Tev) '02
FIG. 58. Contours of (~/s }dW/d~ for uu interactions in pp
collisions according to the parton distributions of Set 2. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
—1
10 10
10 4s (Tev)
FIG. 60. Contours of (~/s)dW/d~ for ug interactions in pp
collisions according to the parton distributions of Set 2. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
Rev. Mod. Phys. , Yol. 66, No. 4, October 1984


Eichten et al. : Supercollider physics
I I I I I II I 1 I I I 1 I 1 I I I I I
I I I I I II
PP(gg) 10 pp(uo)
Set 2 Set 2
—2
10 I I 1 I . I I I I 1 I I. 1 1 I I
—1
10 I I I 1 I 1 1 I I 1 I I I I I
10
10 (Tev) FIG. 61. Contours of (~/s)dW/d~ for gg interactions in p+—p
collisions according to the parton distributions of Set 2. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
10
10 Vs (TeV) FIG. 63. Contours of (v./s)dW/d~ for ud or ud interactions in pp collisions according to the parton distributions of Set 2.
Lines correspond to 10, 10, 10, 10, 1, and 0.1 pb.
different sets of distribution functions. The differences can be seen by comparing Figs. 82(a) (Set 2) and 82(c) (Set 1). There we have plotted recent data from the UA-1 experiment (Arnison et al., 1983d) and the UA-2 experiment
(Bagnaia et al., 1983a,1984). The errors plotted there are
statistical only. For the UA-1 data, there is in addition a
+7.5% uncertainty in the pq scale, which has the effect
of an overall normalization uncertainty of a factor of
(1.5) +—'. The overall additional systematic uncertainty in
the UA-2 data is +40%. The precise agreement between the data and our calculation is thus better than one has a
right to expect. If the scale Q is increased —say, to
pz —then the cross section falls slightly. This can be seen
in Fig. 82(b). This effect is less important at higher energies.
The presence of t-channel and u-channel poles in the elementary cross sections &tj means that at fixed values of s, the cross sections are peaked in the forward and back
ward directions in the parton-parton c.m. , which is to say
at large values of y'. For a fixed value of, p1 the mean
values of x, and xb increase at large values of y*. The consequent fall in the parton distributions tends to reduce the peaking in the elementary cross sections. Figures
84 —89 show the quantity do. /dpqdyb „dy* for fixed
values of yb „and pz. As yb „ increases for fixed
values of y* and p1, x, increases and xt, decreases [cf.
Eqs. (3.5) and (3.6)]. Because of the rapid decrease of the
parton distributions at large x (faster for gluons than for valence quarks), this causes the cross sections to fall, and moreover changes the relative contributions of different
I 1 I I 1 11 I 1 I 1 1 1 I I 1 1 1 11 1 I 1 I I 1
PP(uu) ,0 PP(uu)
I0
Set 2 Set 1
—1
10 I I 1, 1 1 I I
—1
10 I I I I I I I I I I 1 I 1 I 1
10
10 (TeV)
FIG. 62. Contours of (~/s)dW/d~ for uu interactions in pp
collisions according to the parton distributions of Set 2. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
10 10
(Tev)
FIG. 64. Contours of (z/s)dW/d~ for uu interactions in pp
collisions according to the parton distributions of Set 1. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
Rev. Mod. Phys. , Yol. 56, No. 4, October 3984


Eichten et al. : Supercollider physics 605
I I I I I II I
I I I I I II I I I I I I I
10 PP(ud) io — PP(99)
Set 1 Set 1
10-1 I I I I I I —1
10 I I I I I I I I I I I I I I I
10 10
vi (TeV) FICx. 65. Contours of (~/s)dW/d~ for ud interactions in pp
collisions according to the parton distributions of Set 1. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
102
10 vs (Tev}
FIG. 67. Contours of (~/s)dW/dz for gg interactions in p —+p
collisions according to the parton distributions of Set 1. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
final states.
This effect is exhibited in Figs. 84 —86 for pz ——1
TeV/c. At yb „——0, the gluon-gluon final state dom
inates in the neighborhood of y' =0, but at yb „——2 the
gluon-quark final state dominates over the entire rapidity range. As both yb st and pi increase further, the two
quark final state becomes dominant, as illustrated in Fig.
87 for yb „——0 and pi ——5 TeV/c.
Figures 88 and 89 enable a comparison of jet production in pp and pp collisions. As for the integrated cross
sections, the differences are not gross. The ability to select different final states by varying ra
pidity and transverse momentum could be of great importance. As we remarked in the introduction to this section, a complete description of hadronization in QCD has not
yet been achieved. For the moment we have perturbative suggestions, but do not know the consequences of nonperturbative effects. In addition to the results, on jet size
mentioned in Sec. III.A, perturbative QCD indicates that gluon jets should yield a higher hadron multiplicity than quark jets (Mueller 1983a,1983b; Furmanski et al., 1979).
The experimental sample at present consists of predom
inantly quark jets from e+e annihilations and a mixed sample from the CERN collider. The exact nature of the mix is in principle dependent on the structure functions. As can be seen from Figs. 82(a) and 82(c), at any given value of pi, the mix is quite similar at 540 GeV for the
two sets of structure functions we consider. A prelimi
nary comparison between e+e jets and CERN collider jets (Arnison et al., 1983e) reveals no overt differences. In
10
I I I I I II
pp(u9)
I II
' I I I I lr
r 10
I I I I I II
PP(uu)
I I I I I II
Set l Set 1
—1
10 10
II
ve (Tev) 10
—1
10 I I I I I I I-I
10
I I I I I II
Qs {Tev)
FICx. 66. Contours of (~/s)dW/d~ for ug interactions in pp
collisions according to the parton distributions of Set 1. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
FICx. 68. Contours of (~/s)dW/d~ for uu interactions in pp
collisions according to the parton distributions of Set 1. Lines
correspond to 10, 10, 10, 10, 1, and 0.1 pb.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


606 Eichten et ai.: Supercollider physics
I I I I I I I I I I I II
io — pp(ud) t jokOOaa
FIG. 70. Lowest-order Feynman graph for the reaction
q;qj ~ q;qj. (or qiqj~ q;q~, ij ) in QCD.
Set 1
10-1 I I I I I I I
vs (Tev) FIG. 69. Contours of (~/s)dW/dw for ud interactions in pp
collisions according to the parton distributions of Set 1. Lines
correspond to 10", 10, 10, 10, 1, and 0.1 pb.
order to make an incisive comparison, it is essential to remove from the putative large-p~ jets particles associated with beam fragments in pp collisions. Any procedure for
assigning particles to beam jets and to high-pq jets neces
I
—Y&y&,y2 & Y,
then the invariant mass spectrum is given by
(3.17)
sarily introduces ambiguities into the resulting fragmenta
tion function at small values of z:Eh,d,»—/E;„, and will
particularly affect the determination of multiplicity. Complementary data from a common source (e.g., gluon
jets from e+e —+toponium —+ggg or a clean sample of quark jets in p +—p scattering) would greatly advance the
study of hadronization. Another interesting observable is the distribution of
two-jet invariant masses ~. If we constrain the rapidities
of both jets to lie in the interval
Y ~max
f
dyI f dyzg, [f' (x„M )fj' '(xb, M2)&; (s,t,u)
d~ 2 —r &min " ( 1 +Q, . )g cosh2y+
+fj'(x„M )f "'(xb,M )& J(s,u, t)]j, (3.18)
where
y;„=max( —Y,lnr y I ), 
y,„=min(Y, —inc —yi) . (3.19)
The restriction to central rapidities is necessary to avoid the "collinear" singularities arising from t-channel and u-channel poles in o.;J., as well as to circumvent the exper
imental difficulty of particles associated with jets escap
ing down the beam pipe.
Figures 90—92 show the mass spectra der/d~ with
Y = 1.5 for pp collisions at 10, 40, and 100 TeV using the
parton distributions of Set 2. Again we have plotted the contributions of the gluon-gluon, gluon-quark, and quark-quark final states. The results are changed by less
than 10%%uo over the range shown if the parton distributions of Set 1 are used, and there is little difference at these energies between pp and pp collisions. In Figs. 93
and 94 we show the two-jet mass spectra for pp collisions
a
FIG. 71. Lowest-order Feynman graph for the reaction
qiq; ~qjqj. , l +J, ln QCD.
FIG. 72. Lowest-order Feynman diagrams for the reaction q;q;~q;q; in QCD.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 607
FIG. 73. Feynman diagrams for the reaction q;q;~gg, in
lowest-order QCD.
FIG. 75. Lowest-order Feynman diagrams for the reaction
gq ~gq (or gq —+gq) in QCD.
at 540 GeV and 2 TeV, with a tighter rapidity cut given
by F=0.85. Also shown in Fig. 93 are the data of the UA-2 experiment (Bagnaia et al., 1983a). As in the case
of the transverse momentum cross sections of Figs. 82(a) and 82(c), the dependence on structure functions is rather mild. Considering the +40%%uo normalization uncertainty carried by the data, the agreement is quite satisfactory. These jet-jet mass spectra represent a background for any new particles, such as new gauge bosons or Higgs bosons, that decay into jet pairs. We shall refer to them in assess
ing the observability of new phenomena.
where M =~s and 0 & xk & 1, so that
X1+X2+X3=2 . (3.22)
p; = (1;sin8 cosy, sin8 sing, cos8),
2
The normal to the plane defined by p~, pz, ps, makes an
angle 8 with the beam direction. The azimuthal orientation of the normal is specified by the angle y. The four
momenta of the incoming and outgoing partons may be expressed as
C. Multijet phenomena
At order a, in @CD occur two-body to three-body sub
processes such as gg —+ggg which can give rise to three
jets with large transverse momentum. Because of the kinematical richness of this topology (five independent
variables for the 2~3 reaction plus one for motion relative to the lab frame), a full simulation is for many purposes indispensible. However, - more restricted calculations have great value for orientation, and we will restrict our attention to questions that may be addressed without Monte Carlo programs. In order to describe the elementary reaction, it is convenient to label the momenta of the participating partons as indicated in Fig. 9S and to use the coordinates introduced by Sivers and Gottschalk (1980). We work in the
c.m. frame of the three-jet system, defined by the condition
p~ = (1;—sin8 cosy, —sin8 sing, —cos8),
x)~
pi —— (1;1,0,0),
2
X2M
pz —— (1;cos8)~,stn8tz, 0),
2
X3~
ps —— (I;cos8&3, —sin8, 3 0)
where Okl, the angle between pk and pi, is given by
cos8ki = 1 —2(xk +x~ —1)/xkxi .
(3.23)
(3.24)
pl+ p2+ P3 (3.20)
In this frame the energies of the individual jets may be written as
Ek =xk~/2, k =1,2, 3, (3.21)
FIG. 74. Feynman diagrams for the reaction gg~q;q;, in
lowest-order QCD.
FIG. 76.' Lowest-order Feynman diagrams for gluon-gluon elastic scattering in QCD.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


608 Eichten et aI.: Supercollider physics
Xb t =O'I+Z2+Z3)/3 (3.25)
I
An additional variable is needed to completely describe the system. An apt choice is the rapidity
of the three-jet system in the c.m. frame of the colliding hadrons. After these preliminaries, we may write the three-jet cross section as
dx Idx2dyb, d~ d Q
where r=~ /s and as usual
3 2 [f '(x„M )fj '(xs, M )Atj+f~"(x„M )f '(xb, M )AJ&],
77~ » + gj
(3.26)
x. =3/ re ', x, =V ~e (3.27)
The quantity A;z is the absolute square of the invariant amplitude for the process depicted in Fig. 95. The matrix ele
ments for the processes of interest have been given in compact form by Berends et al. (1981). There are four basic processes to be considered. For the elementary reaction
(pl)+q (Pj )~q~(PI )+q (P2)+g(P3)
the result is
(3.28)
A =F(p p, PI,P2 p3),
where
(3.29)
s +s' +u +u'
F(k;,kj, kI, k2, k3)= {C,[(u+u')(ss'+tt' uu')+u(s t~—s't')+u'(st'+s't)]
st t'k-3k, 3k13k.3
—C2[(s+s')(ss' —tt' —uu')+2tt'(u+ u')+2uu'(t+ t')] I, (3.30)
with
CI ——16/27, C2 ——2/27,
kmn km kn
s=(k;+kj), s'=(kI+k2)
t=(k; —k, )', t'=(k; k, )', 
u =(k; —k2), u'=(k~ —kI)
For the scattering of identical quarks,
q (p;)+q„(p, )~q„(PI)+q (p2)+g(p3),
the exchange terms make for additional complexity. In this case the result is
(P& &Pal &P I &P 2 &P 3 )
where
F'(k; k &kj»&k k2&)=3F(kt&kj&kI&k2&k3)+F(k&&kj&k2&kI&k3)
(3.31)
(3.32)
(3.33)
+ {C3[(s+s')(ss'—tt' —uu')+2tt'(u+u')+2uu'(t+t')]
kj 3kj3k $3k23
+C4[(s+s')(ss' —tt' uu') —2tt '—(u +u') —2uu'(t+t')
—2s (t u+t'u ) —2s (tu'+t'u)]j, (3.34)
3The more complicated formulas given by Sivers and Gottschalk {1980)appear to contain typographical errors.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 609
with
C3 ——10/81, Cg ——8/81 .
For the three-quantum annihilation reaction
e (Pi)e (PJ) g(P1)+g(P2)+g(P3»
the square of the amplitude is
H(PI pPJ PP1 ~P2~P3 )
where
H(k k k k k ) 2,.i,l(,i+ i) s s (lJ.12)
81 i, k(1k;2ki3kiiki2kq3 2 2 k12
(ij;13)
k)3
(ij;23)
k23
(3.35)
(3.36)
(3.37)
81 (ij;33)(ij;12) (ij;11)(ij;23) (ij;22)(ij;13)
++
+ S k13k23 k 12k 23
(3.38)
where
where
G (Pl lPJ 9P 1 &P 2 ~P 3 )
(ij;mn)=k; kz„+k;„kz
Finally, for gluon-gluon scattering
g (P;)+g(P,.) g(P1)+g(P2)+g(P3)
the result can be.written as
(3.39)
(3AO)
(3A1)
The squared matrix elements for all the other 2~3 reactions may be obtained from these results by crossing
symmetry. They are listed in Table I. Notice that symmetry factors have not been included when there are identical particles in the final state. For the numerical results presented below we assume that the detector does not distinguish between quark or antiquark jets and gluon jets. As a result, we sum over the contributions for all permutations of the final-state momentum assignments to distinguishable particles. %'e have chosen the scales appearing in (3.26) as
G(k;, k/, k„k2,k3) = g (ij 123),
160 k~„ (3A2)
with
m&n
(ij 123)=—k;, k, ,k»k23k3j . (3.43)
Here the indices m and n run over i,j,1,2;3, and for the
restriction m & n we interpret i &j & 1.
TABLE I. Squared matrix elements A;j of Eq. (3.26) for 2~3 processes in QCD. The labels m and n refer to quark flavors; repeated indices are not summed. The results are averaged over initial-state spins and color, and summed over final-state spins
and colors. The functions F, F', G, and H are defined in Eqs.
{3.30), (3.34), (3.42), and {3.38), respectively.
Process
ij ~123
-3
10
-4
io
LV 10
9
L
XCl -1
10
-3
10
'0
'00
qmqn ~qmqng qmqm ~qmqmg qmqn ~qmqng qna qm ~qmqmg qmqm ~qnqng qmg ~qm qn qn 9mg~qm qm qm gg~ggg
qmqm ~ggg qmg~qmgg gg~qmqmg
F(pi pj~pt p2~p3)
F (pi pj~pi p2~p3)
F(pi,p2, —pi, —pj,p3)
F
(pg ~ —p2~p1» —pj~p3)
F(p —p» —p p2p3)
3
8 )F(pi& p3&plxp2& pj )
( —8 )F'(p;, —p3,p),p2, —p )
G(pi pj~pi p2~p3)
II(Pi Pj~Pi P2~P3)
3
( ——)&(P- —P~ —P- P2 P3) 9 P2 P& Pj P' P3)
10 0.2 O. B 1.e
(TeV/c) FIG. 77. Differential cross section (solid line) for jet production
at y =0 (90 c.m. ) in pp collisions at 10 TeV, according to the
parton distributions of Set 2. The gg (dotted-dashed line), gq (dotted line), and qq (dashed line) components are shown separately.
Rev. Mod. Phys. , Vol. 56, No, 4, October 1S84


610 Eichten et al. : Supercollider physics
10 10
I
V 10
VL0
C
-3
10
u 10
CL 10
'b0
I
~
LV
V
DC
CII)
'0~l
'Qb
10
-2
10
-3
10
10 —4
10
-5
10 -5
10
-6
10 -B
10
-7
10 0.5 1.5 2. 5 3.5 4. 5
-7
10 0.5 1.6 2.5 3.5 4 ' 5 p, (Tev/~)
FIG. 78. Differential cross section for jet production at y=0
(90 c.m. ) in pp collisions at 40 TeV, according to the parton dis
tributions of Set 2.
p, (Tev/c)
FIG. 80. Differential cross section for jet production at y =0
(90 c.m. ) in pp collisions at 40 TeV, according to the parton dis
tributions of Set 1.
10 10
10
C3
CCh
10
10
b 10
V 10
L
1
a CCl -1
O 10
II
-2
10
CL
b 10
10 -4
10
10 -5
10
10 -B
10
10 -7
10 0.2 O. e 1.4 1.8 p, (Tev/c)
FIG. 79. Differential cross section for jet production at y=0
(90 c.m. ) in pp collisions at 100 TeV, according to the parton
distributions of Set 2.
p, (Tev/c)
FIG. 81. Differential cross section for jet production at y =0
(90' c.m. ) in pp collisions at 10 TeV, according to the parton dis
tributions of Set 2.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics
10
10 2
C09) 10
nO
~l 10 '=
1 n
~ 10'
10 10
10 10
10"0
tt t l
50 p (GeV/c)
100 150 10'0 50 p (GeV/c)
100 150
I I- i I I I I i I I I I
103
102
pp —jet+ X
vs = 540 GeV
~ UA2 Bagnaia et al. (1984)
o UA2 Bagnaia et al. (1983a) =
~UA1 Arnison et al. (1983b)0 UAl Arnison et al (1985d)
IOI
a
CC3L
o
10
10
10+0 100 150 p (GeV/c)
FICx. 82. Differential cross section for jet production at y =0 (90 c.m. ) in pp collisions at 540 GeV, (a) according to the parton distri
butions of Set 2; (b) with the scale Q2=M~=pj,' (c) according to the parton distributions of Set 1. The data are from Arnison et al. (1983d) and Bagnaia et aL (1983a,1984).
Q =M =~/4; (3.44)
as noted in Sec. III.B, they are undetermined to this order ln Ag. The three-jet cross section becomes singular as xk, the
fractional energy of any jet in the c.m. frame of the three-jet system, approaches zero or one. In the former
case the zero-energy jet cannot be distinguished. In the latter case the remaining two jets become parallel and coalesce. Either configuration will be identified as a twojet event. The most characteristic three-jet events are those in which three jets of equal energies are emitted at 90 in the
colliding beam c.m. frame. In terms of the kinematic
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


612 Eichten et af.: Supercollider physics
10 10
LO
V
CCh
D
b.
10
-1
10
1.0
-3
10
O
0 1O-4
C
DQl
1O I-'
-4
10
-5
10
1O-' /
I
—2
~s - 40 Tev
-8
io
-7
10 0. 1 0.8 0.3 0.4 0.5 0.6
FIG. 85. Differential cross section. for jet production in 40-TeV
pp collisions, for yb, „,——1 and p& ——1 TeV/c, according to the
parton distributions of Set 2.
P, (TeV/c)
FIG. 83. Differential cross section for jet production at y=0
(90 c.m. ) in pp collisions at 2 TeV, according to the parton dis
tributions of Set 2.
ET ——M . (3.45)
variables introduced above, this corresponds to the pa
rameter values x~ ——x2 ——x3 ———,, yb „——0, and 0=0. We
show in Figs. 96—99 the differential cross section
do/dx~dx2dyb, d~d(cose) for this symmetric configuration at four collider energies. (In this situation the cross section does not depend upon the azimuthal angle y,
so the y integration has been performed. ) In events of
this kind, the total transverse energy is
One measure of the relative importance of two-jet and three-jet events may therefore be obtained by comparing the symmetric three-jet cross section with do'/dpydp ~ & p
for the two-jet case, evaluated at pz ——~/2. This
amounts to comparing two-jet and three-jet events with the same transverse energy. To make the comparison, it is necessary to integrate the three-jet cross section over appropri. 'ate intervals in x&, x2, and cos8. One typically
finds that at the same value of ET, the two-jet cross sec
tion is larger by 1 —2 orders of magnitude than the threejet cross section. Of course, this particular three-jet con
figuration is in some sense the smallest, since the x;'are well away from the singular regions. The contributions from the distinct final states (ggg,
lo 1O-'
O
10 4
1O-'
pp ~ jet
~s = 40 Tev
1O-'
I /
I
/
I I/ I
pp ~ jet + anything
~s ~ 40 Tev
1O-' —3
10 —0.8 0.8
FIG. 84. Differential cross section for jet production in 40-TeV
pp collisions, for yb „—0—and p& ——1 TeV/c, according to the
parton distributions of Set 2.
FIG. 86. Differential cross section for jet production in 40-TeV
pp collisions, for yb„„——2 and p& ——1 TeV/c, according to the
parton distributions of Set 2.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 613
10 7 .r
1O-'
e 10
V
1O-' 10
10—10
l
I pp -~ jet + anything
/
vs 40 TeV 40 TeV
1O-" —1I.6 —0.8 0 0.8 1.6
10 8 —1.I6
—0I.8 0 0.8 1.6
FICx. 87. Differential cross section for jet production in 40-TeV
pp collisions, for yb „——0 and p& — —5 TeV/c, according to the
parton distributions of Set 2.
FIG. 89. Differential cross section for jet production in 40-TeV
pp collisions, for yt „,——0 and pj =3 TeV/c, according to the
,parton distributions of Set 2.
( —) ( —)( —) ( —)( —)( —)
gg q, g q q, and q q q ) are shown separately in the
figures. At values of M small in comparison with v s,
corresponding to parton momentum fractions
xg =xb =M/Vs ((1 (3.46)
10—6 V
the process gg~ggg dominates. Just as in the two-jet
events, the final state consists almost exclusively of gluon
jets. As ~ increases, the process gq~ggq becomes im
portant and eventually dominant. The three-quark final state is always negligible. Because of the preeminence of gg and gq collisions, differences between pp and pp col
lisions at the same energy occur only at the 10% level. Some insight into the variation of the cross section with xt and x2 may be gained from Fig. 100, which shows
10
1 oe0
10
4&
C
—1
10
O -8
10
the differential cross section ' drJ/dx&dxqdyb „dM
Xd(cos8) at x t ——0.3 and x =0.8 (so that x3 ——0.9), still
with yb „=0 and cos8=1, for pp collisions at 40 TeV.
This is close to the limiting situation in which the third jet ceases, to be identifiable. The cross section is larger by
about a factor of 3 than for the symmetric configuration, and the three-jet to two-jet ratio is correspondingly larger, but the relative importance of the different final states is essentially unchanged.
D
10
—3
10
—4
10
—6
10
1O-' I
I
—1.6
I
—0.8
I
0
I
0.8
II
1.6
FIG. 88. Differential cross section for jet production in 40-TeV
pp collisions, for yb „——0 and p& ——3 TeV/c, according to the
parton distributions of Set 2.
1.2
10 I I I I I I I I I
'
0.4 2 2. 8 3.6
Jet Pair Mass (TeV/c*) FIG. 90. Invariant mass spectrum for two-jet events produced
in proton-proton collisions at V s =10 TeV, according to the parton distributions of Set 2. Both jets must satisfy ~ y; ~ & 1.5.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


614 Eichten et al. : Supercollider physics
2
iO
l I ~ ~1I l ~ ~ 1~~ ~I 1 ~ & I~ 1 ~ I I I 1 Il I I
NV
10
VL0
C
x 10
Xbl 10
10 3
10
10
O
0)
1
jet + X GeV
g et al. (1984)
a et af. (1983a)
10 CG CV) 10
10
IO
10
10
10
-7
10
4 5 e 7 8 9 10
Jet Pair Mass (TeV/c )
FIG. 91. Invariant mass spectrum for two-jet events produced
in proton-proton collisions at Vs =40 TeV, according to the parton distributions of Set 2. Both jets must satisfy ~ y; ~ & 1.5.
0
1i i i~ I» ii I i s si I
100 200 & (GeVZc')
I
300
FIG. 93. Invariant mass spectrum for two-jet events produced
in proton-antiproton collisions at ~s=540 CreV, according to the parton distributions of Set 1. Both jets must satisfy ~ y; ~ &0.85. The data are from Bagnaia et al. (1983a,1984); errors are statistical only.
10
r
V
10
VO
1
C
—1
Q 10
'Q -2
10
10
ee0
10
V4
10 C
—1
10
-3
10 -2
10
10 -3
10
10 10
10 10
1, 0 e S 10 12 14
Jet Pair Mass (TeV/c )
10 0. 1 0.3 , 0.5 0. 7 0. 9
Jet Pair Mass (TeV/c')
FIG. 92. Invariant mass spectrum for two-jet events produced
in proton-proton collisions at V s =100 TeV, according to the parton distributions of Set 2. Both jets must satisfy ~ y; ~ & 1.5.
FIG. 94. Invariant mass spectrum for two-jet events produced
in proton-antiproton collisions at V s =2 TeV, according to the
parton distributions of Set 2. Both jets'must satisfy ~ y; ~ & 0.85.
Rev. Mod. Phys. , Vot. 56, No. 4, October 1984


Eiehten et a/. : Supercollider physics
tlV
C
10
10
Flax. . 95. A generic 2~3 process in QCD.
Os
'lV00A
&'0X &X
'b0
1
-1
10
-2
10
-3
10
-4
10
As the plane of the three jets approaches the beam direction pvith other kinematic variables held constant, the cross section increases, as shove in Fig. 101. This resu1ts
from the approach to the collinear singularities in A,J at
t=0, etc.
To determine more meaningfully the dependence of the cross section upon the orientation of the event plane we must impose some experimental cuts to ensure that all the jets are distinct. As an example me show in Fig. 102 the
three-jet cross section at yb „——0 and ~=1 TeV/c,
subject to the requirements that each jet has an energy of
10
10 0.6
0. 1 0.3 0. 7 0.8 M (TeV/c')
FIG. 97. Differential cross section for symmetric three-jet production in pp collisions at 2 TeV, according to the parton distri
butions of Set 2.
10
e~
IVV 10
V0
10 C
os
OV0l
10
'Q
OO -8
10 C'0X
&X 3
10
'Qb
10
OIVLV0
XCh
0
'NV00
NOO
'0 &'0X
C'0X
'b0
10
10
-8
10
-4
10
~3
10
3
io
10 1 l I l I
10
0.04 0.08 0. 18 0. )8 0.2 0.24 0.88 M (Tev/c )
FIG. 96. Differential cross section (thick line) for symmetric 3-jet production in pp collisions at 540 GeV, according to the
parton distributions of Set 2. The ggg (dotted-dashed line), ggq
(dotted line), qqg (thin line), and qqq (dashed line) components
are shown separately. 
-B
10 0.4 O. a 1.2 3 2.4 M (Tevlc )
FIG. 98. Differential cross section for symmetric three-jet production in pp collisions at 10 TeV, according to the parton dis
tributions of Set 2.
Rev. Mod. Phys. , Vot. 56, No. 4, October 1984


ElchteA et 8/. : SUpel coIIlder phYslcs
10
eIO
C
10
1
eeU
0
JCD
s
(V00A
'Q o0
&0X
CX0
'U
-2
10
-3
10
-4
10
—5
10
0
tA
O0 10 0 '0
OO
10
i&lx3Xcv
b
10
-6
10
—7
10
B
M (Tev/c')
0. 1 0.3 0.5 0.7 0, 8 cosO
FIG. 99. Differential cross section for symmetric three-jet production in pp collisions at 40 TeV, according to the parton dis
tributions of Set 2.
FIG. 101. Dependence upon the orientation of the three-jet plane of the differential cross section for symmetric three-jet production in pp collisions at 40 TeV, according to the parton
distributions of Set 2. The invariant mass of the three-jet sys
tem is ~=1 TeV/c ~
1 ~v0
Q0
C
0
l/U0I
'U
'0
OO
'0
&0X
&0X
'Q
10
10
1
-1
10
-8
10
-3
10
-4
10
—5
10
no less than 50 GeV, and that the angle L9~„between any
pair of jets or any jet and the beam direction exceeds 18,
so that cosO „&0.95. These cuts ensure that no jet will be confused with the normal, low-pz beam jets, and also
cut off the rise of the cross section as cos8~0. The re
sulting cross section is concentrated around cos0=0.35. We can compare two-jet and three-jet contributions to do /dEz dy as follows. First, consider the interval
0.9 & cosO & 1 in Fig. 102. The integrated cross section in
this bin is approximately 7X10 nb/GeV, at ET-1
l.5
MO
I0
CD
0.5
b
—7
10
(TeV/c ) 0 0.2 0.4
COS 8
0.6 0.8 I.O
FIG. 100. Differential cross section for production of three jets
at 90 in the c.m. in pp collisions at 40 TeV, according to the
parton distributions of Set 2. The energy fractions of the three
jets are x~ — —0.3, x2 ——0.8, and x3 ——0.9.
FIG. 102. Three-jet cross section in 40-TeV pp collisions in
tegrated over azimuth and the energy fractions xl and x2, subject to the restrictions described in the text. The three-jet invari
ant mass is ~=1 TeV/c-.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et aI.: Supercotlider. physics 617
TeV. From Fig. 78 we find the corresponding two-jet
cross section (at p~ =0.5 TeV/c) to be about 7X10
nb/GeV, which is larger by an order of magnitude. I.et
us next consider the cross section in the neighborhood of the peak in Fig. 102. The integrated cross section in the
bin 0.3(cos8&0.4 is approximately 0.1 nb/GeV, with
transverse energy given roughly by (ET ) =(1 TeV)
X(cos8) =350 GeV. The corresponding two-jet cross section, again from Fig. 78, is approximately 10 nb/GeV, which is larger by 2 orders of magnitude. In fact, we
have certainly underestimated (ET) and thus somewhat overestimated the two-jet/three-jet ratio in this second case. We draw two conclusions from this very casual analysis:
At least at small-to-moderate values of ET, two-jet
events should account for most of the cross section. . The three-jet cross section is large enough that a detailed study of this topology should be possible.
It is apparent that these questions are amenable to detailed investigation with the aid of realistic Monte Carlo simulations. Given the elementary two~three cross sections and reasonable parametrizations of the fragmentation functions, this exercise can be carried out with some degree of confidence. For multijet events containing more than three jets, thetheoretical situation is considerably more primitive. A specific question of interest concerns the QCD four-jet
background to the detection of W+JY pairs in their nonleptonic decays. The cross sections for the elementary
two —+four processes have not been calculated, and their complexity is such that they may not be evaluated in the foreseeable future. It is worthwhile to seek estimates of
the four-jet cross sections, even if these are only reliable in restricted regions of phase space. Another background source of four-jet events is double
parton scattering, as shown in Fig. 103. If all the parton momentum fractions are small, the two interactions may be treated as uncorrelated. The resulting four-jet cross section with transverse energy ET may then be approximated by
o2(ET1)P2(ET2)@ET1+ET2 ET)
cr4(ET )= dET ) dET2 ~total
(3.47)
where crz(ET~) is the two-jet cross section and E denotes the minimum ET required for a discernable two-jet event.
For a recent study of double parton scattering at SppS and Tevatron energies, see Paver and Treleani (1983). In view of the promise that multijet spectroscopy holds, improving our understanding of the QCD background is an urgent priority for further study.
D. Summary
IY. ELECTROWEAK P HENOMENA
In this section we discuss the supercollider processes associated with the standard model of the weak and electromagnetic interactions (Glashow, 1961;Weinberg, 1967; Salam, 1968). By "standard model" we understand the
SU(2)1 SU(l)r theory applied to three quark and lepton doublets, and with the gauge symmetry broken by a single complex Higgs doublet. The particles associated with the electroweak interactions are therefore the (left-handed)
charged intermediate bosons 8' +—, the neutral intermedi
We conclude this section with a brief summary of the ranges of jet energy which are accessible for various beam energies and luminosities. We find essentially no differences between pp and pp collisions, so only pp results will
be given except at V s =2 TeV where pp rates are quoted.
Figure 104 shows the ET range which can be explored at
the level of at least one event per GeV of ET per unit ra
pidity at 90' in the c.m. (compare Figs. 77—79 and 83). The results are presented in terms of the transverse energy per event ET, which corresponds to twice the transverse
momentum pq of a jet. In Fig. 105 we plot the values of ET that distinguish the regimes in which the two-gluon, quark-gluon, and quark-quark final states are dominant. Comparing with Fig. 104, we find that while the accessible ranges of ET are impressive, it seems extremely diffi
cult to obtain a clean sample of quark jets. Useful for estimating trigger rates is the total cross section for two jets integrated over ET(=2pj ) &ET for both jets in a rapidi
ty interval-of —2.5 to + 2.5. This is shown for pp col
lisions in Fig. 106.
FICx. 103. Four-jet topology arising from two independent parton interactions.
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984'


618 Eichten et al. : Supercollider physics
iO C
10 4J 10
'U0
1
3
12 I
10 20 /s (TeV)
I
50 100
10
-7
io 18 14. 16 iB 20
(Tev)
ate boson Z, and an elementary Higgs scalar H .
The principal standard model issues to be addressed with a multi-TeV hadron collider are these.
eThe rate of 8' +—and Z production. This is chiefly of interest for investigations of the production mechanism
2
Is
10 20
Is (TeV)
5I0 100
FIG. 104. Discovery reach of hadron colliders for the observa
tion of two-jet events, according to the parton distributions of
Set 2, for integrated luminosities of 10, 10, and 10 cm
FIG. 106. The tota1 cross section for two jets integrated over y~
and y~ and ET (=2 pr) subject to the constraints ~y~
~y2 ~ &2.5, and Er&ET as a function of Er for various s,
00
according to the parton distributions of Set 2.
itself and for the study of rare decays of the intermediate bosons. We expect that by the time a supercollider comes into operation more basic measurements, such as precision determinations of the masses and widths of the intermediate bosons, will have been accomplished. oThe cross sections for pair production of gauge bo
sons. These are sensitive to the structure of the trilinear couplings among gauge bosons, and must be understood as potential backgrounds to the observation of heavy Higgs bosons, composite scalars, and other novel phenomena. They would also be influenced significantly by unconventional strong interactions among the gauge bosons
(Veltman, 1983). oThe Higgs boson itself. In the standard electroweak model, this is the lone boson remaining to be found. As we have emphasized in the Introduction, elucidating the
structure of the Higgs sector is one of the fundamental
goals of experimentation in the TeV regime. We now shall treat in turn the conventional phenomena associated with the standard model. For each of them we shall briefly review the physics interest and discuss the
anticipated rates. In the case of the Higgs boson, we shall pay particular attention to the prospects for observing and
making sense of the expected experimental signatures.
A. Dilepton production
FICr. 105. Parton composition of the two-jet final states pro
duced in pp collisions at 90' in the c.m. The curves separate the regions in which gg, gq, and qq final states are dominant.
In the context of the 1-TeV scale, the reaction
p +—p —+l+l +anything (4 I)
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et ai.: Supercollider physics 619
qq ~y*~l+1 (4.2)
is chiefly of interest as a source of background to searches for heavy quarks and other objects and as a window on perturbative QCD calculations. The elementary process we consider is the lowest-order Drell-Yan (1970,1971) mechanism,
color: the quark and antiquark that annihilate into a virtual photon must have the same color as well as flavor. In high-energy collisions it is frequently convenient to
work in terms of the c.m. rapidity variable ' E(c.m. )+ (c.m. )
ln E(c.m. ) (c.m. ) (4.8)
illustrated in Fig. 107. The differential cross section for
the production of a lepton pair with invariant mass M in
the reaction a +b +I+—I + anything is given by
which is related to x, x„and xb through
x =2~~sinhy, (4.9)
dCT
dM dx
8m'a E(~,x,M~),
3M (4.3) x. , =V ~e
The differential cross section is given by
(4.10)
where the function do 2 4 ty2 dQ'
I"(r,x,M )= 2,i2 g (x„xb,M )
(x'+4~)'"
depends upon the scaled variables
' 8@a vg(V re~, Wee ",M ) .
3M (4.1 1)
and
v =M2/s (4.5) The integrated cross section for dilepton production is
T
Sn-a ' dxg(x, ~/x, M ) 3M X
(c.m. ) /~
ll
in the combinations
(4.6) S~a', «~ir
9M' (4.12)
x, b ——', [(x +4r—)'~+x] . (2.8)
Information about the quark-antiquark luminosity is contained in the function
g (x.,x,,M') = ', g e,'[—f", (x.M')f;''(xb, M').
Qavors
+f''(x M )f' '(x -M )]
(4.7)
where e; is the charge of quark flavor i in units of the
proton charge and f (x„g ) is the number distribution
of i quarks in hadron a. The factor —' , is a consequence of qq ~Zo~l+l (4.13)
This may readily be done by making the replacement
M'(M' —M.')(L, +R, )(L, +R, )
Sx~(1—xw)[(M' —Mz) +MzI z l
Apart from the gentle M dependence of the differential luminosity which arises from scaling violations in the parton distributions, the quantity M do /dM is a function of the dimensionless variable ~ alone. Although there are important strong-interaction corrections to the parton model for this process, the scaling behavior has been established experimentally to good approximation. At the masses which have been accessible in experiments to date, the virtual photon mechanism of Fig. 107 is an adequate approximation. At higher masses it is necessary to 'include the contributions of a real or virtual neutral intermediate boson in the elementary process
M (L~+R~)(Lq+Rq)
64xw(l —xw) [(M —Mz) +Mzl z] (4.14)
in the definition of g(x„xb, Q ) in Eq. (4.7), and in (4.12).
Here the chiral couplings of the neutral weak current are
I., =2Xp —1,
Rg —2Xgf
(4.15)
I'IG. 107. Drell-Yan mechanism for massive lepton-pair production in pp collisions.
4See, for example, the data compiled in Fig. 7-15 of Quigg (1983}.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


620 Eichten et a/. : Supercollider physics
for the electron (or sequential charged lepton) and
L(q —73 2' X~ (4.16) ing
GFMz'v 2
rz 3' Sxp2
1 —2xp + 3 D, (4.17)
where D is the number of kinematically accessible quark and lepton doublets and
Rq — 2' x ~
for the quarks, where ~3 is th|: weak isospin projection of
the quark and x~ ——sin 0~ is the weak mixing angle. In
the standard model, the width of the Z is
10
Q
LCh 6
10
II
—7
'0 10
'U
Mz ——M~/(1 —xg ) = GF 2xp (1 —xII )
=(37.3 GeV/c ) /xp (1 —x~) . (4.18) 10
With x~ ——0.22 and D =3, we expect
z -90 GeV/e2 (4.19)
-10
10 0.6 Mass (TeV/c')
I z=2.6 GeV .
The partial width into charged lepton pairs is
3
GFMz 2
I (Z ~l+l )= (1 —4xp+8xg )
12m 2
(4.20)
FIG. 108. Cross section do/dM dy ~ ~ o for the production of
lepton pairs in proton-proton collisions. The contributions of
y* and Z intermediate states are included. The energies shown are 2, 10, 20, 40, 70, and 100 TeV. Set 2 of parton distributions was used.
=(1—4xII +8xII )I (Z ~vv) . (4.21)
W'ith x~ ——0.22 and D =3, the branching ratio into a pair
of electrons, muons, or taus is approximately 3%.
We display in Fig.' 108 the quantity do/dMdy ~»
for pp collisions at c.m. energies of 2, 10, 20, 40, 70, and
100 TeV. The cross sections shown are based on the parton distributions of Set 2. In general we shall present results only for Set 2, unless the two sets yield significantly different cross sections. For an integrated luminosity of
10 cm, we anticipate a yield of one event per GeV/c
per unit rapidity for
300 GeV/c at Vs =2 TeV 500 GeV/c at Vs =10 TeV 600 GeV/c at Vs =20 TeV (4.22)
700 GeV/c at Vs =40 TeV 800 GeV/c at Vs =70 TeV ,850 GeV/c 2 at V s =100 TeV .
The energy dependence of the cross section, and thus of the maximum attainable pair mass, can readily be inferred from the contour plot Fig. 63 of the rate of uu interactions in pp collisions, using the connection of Eq. (4.12).
The Drell-Yan cross section for pp co11isions is reported
in Fig. 109. The yields are slightly, but not significantly, higher than those expected in proton-proton collisions. The Drell-Yan mechanism operates for the pair pro
10
LV 10
V
Cl
10
CI II
'U — 7
D 10
D
—a
KO
9
10
—10
10 a, s 1.5 2. 5 3.5 4. 5
Ma ss (TeV/c*)
Flay. 109. Cross section do/dM dy ~ ~ o for the production of
lepton pairs in proton-antiproton collisions. The contributions
of y* and Z intermediate states are included. The energies shown are 2, 10, 20, 40, 70, and 100 TeV. Set 2 of parton distributions was used.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : SUpercollider physics 621
duction of any pointlike charged lepton. If the lepton mass mL is not negligible compared to the pair mass M,
there is a kinematical suppression of the cross section in
the form of an additional factor (1 —4mL /M )'~ X (1+2mL, /M ). This is discussed in detail in Sec. V.
Within the framework of QCD there are additional contributions to dilepton production, such as the elementary process
g+q~(y or Zo)+q
l+I (4.23)
as well as strong-interaction corrections to the basic Drell-Yan mechanism. Although these do not alter our conclusions qualitatively, they do have interesting consequences for the rate, the transverse momentum distribution, event topology, and other features. The state of the art is summarized in the workshop proceedings edited by Berger et al. (1983).
B. Intermediate boson production
7TCX
GF~~ W
(37.3 GeV/c ) (4.24)
where x~ ——sin 8~ is the weak mixing angle. The lepton
ic decay rate is
The intermediate bosons of the standard model, which set the scale for the current generation of colliders, will still be of interest at a supercollider for calibration and backgrounds, and for the study of rare decays. The conventional expectations for the discovery of the intermediate bosons were set out in detail in papers by Quigg (1977) and by Okun and Voloshin (1977). An up-to-date review has been given by Ellis et al. (1982). The first observa
tions of the W +— and Z have been reported by Arnison et al. (1983a,1983c), Banner et al. (1983), and Bagnaia et al. (1983b). We recall that in the standard model the mass of the charged intermediate boson is given in lowest order by
Here we have ignored quark masses and mixing angles. For the weak mixing parameter
xg ——0.22,
a plausible value, we find
Mw-81 GeV/c
and
I ( W~l v) =250 MeV .
(4.28)
(4.29)
(4.30)
Consequently, for three doublets of quarks and leptons we anticipate a total width of
I ( W~all)=2. 8 GeV . (4.31)
32
(1—cos8), A, w ——1
16m.
32
sin 8, Ag ——0
8m
(1+cos8), Xw —
32 16m
(4.32)
where A, w is the helicity of the W +—and 8 is the angle be
tween the lepton direction and the 8' spin quantization axis in the W rest frame. The cross section for the reaction
There are radiative corrections to these masses and widths in the standard model which depend upon the masses of quarks and leptons (Marciano, 1979; Antonelli, Consoli, and Corbo, 1980; Veltman, 1980; Sirlin and Marciano, 1981; ctheater and Llewellyn Smith, 1982; Marciano and Senjanovic, 1982; Marciano and Sirlin, 1984). In
particular, the ratio p =Mw/Mz(1 —x w) deviates slightly
from one (Veltman, 1977; Marciano, 1979); thi's is used to constrain extra generations of quarks and leptons in Sec. V. The resulting values for the radiatively corrected
masses are (Marciano and Parsa, 1982) Mw ——83.9+47
GeV/c and Mz =93.8 2'4 GeV/c .
The normalized angular distribution of the decay fermion is
r( W lv) = G,M' /6~v 2 . (4.25) a +b ~ S' +—+anything (4.33)
The partial widths for nonleptonic S'+—decays may be related at once to the leptonic width as, for example,
I'( W+ud) =3 cos28, 1 ( W~lv),
I ( W+ —+us ) = 3 sin 8, 1 ( W~l v), (4.26)
where the factor of 3 accounts for quark colors. More
generally, if D~ is the number of color-triplet SU(2) dou
blets of quarks into which the intermediate boson can decay, and Dt is the number of energetically accessible lepton doublets, then the total width is given by
where de ——d cos8, +s sin8, . The differential cross section is given by
dy =GF~v 2~w'+'(~~e&, v ~e Y,Mw), 
(4.35)
can be computed directly in the Drell-Yan picture. In this case the elementary reactions are
I
u +dg —+W+,
(4.34)
1-( W~all) =(D, +3D, )I ( W~lv) . (4.27) where r=Mw/s and
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten eet al. : SUpercollide~ physics
I
for mass and widths were given. The reaction
Quarks and anti qua«s are interchanged for pr
tion. The integrated ~+ o p«duc
cross section is5
a +b —+Z +anything
S"~+'&(X~»b Q )= —«&') 2 (b)
3 I I.fig (xggg )fg (x Q2) +f(a)( 2 (b)
»f. (xb, g')]cos2g,
Lfg (Xgp Q )f (Xb Q2) +f(Iz)( 2 (b) (xbyg )]slil g (4.36)
(4.38)
+—(x,r/x, Mii )
I dx W' +—'x
X proceeds via the elementa ro
en ary processes uu ~ZO, dd ~Z
e i erential cross secti'onn may e written as
Gb. m.~2
3
dW„~ dW„,
cos20, +~ "' sin 0
7 d~ Gb mr Z(V re~, v re ~,Mz), (4.39)
dM
=6.3 nba d7 (4.37)
where r=Mz/s and Integrated cross sections for 8'+- production in
sections for production f W~
. energy s. The figures also show the cross
c ion o 8' —in the ra idit In pp collisions the production
is suppressed relative to 8 + b
because of th
y a factor of 2 or so
e smaller momentum fraction car '
in pp collisions. As '
or and 8' production are nece ssarily equal s in t e case of dile ton the competitive ad t
a vantage o anti rot
~~
The angular distributi f h
ion o t e produced great importance for the d
uc within a narrow ' one
w an uiar cone
e pro
direction. S ec'
pecial-purpose detectors de lo ed
fo di 'o h study of rare d
' n may ave si nific rare ecays. To illustrate this oint w .
Fi . 112( ) th dt di
api ity istribution d(T/d for + o on collisions at 40 TeV
ping from rapidit t . g ' 'v
gg g
' e wi an average luInlnos wi e a ux of a roxim
The n
or pp co lisions are shown in Fi . 114
e nearly complete alignment of 8's i d d ti h
a ic c arge asymmetry in the CE
rgies w oss sectio is
k. [C
i iaions of sea u
Figures 112(b) and 114 b show
an the net helicity of the pro
at s =40 Tev.
Thee analysis of single Z production
~ l, 1 d- p
w ere t e expectations of the standard model
5The subse uent fo
q formulas are given for onl t
tension and were used in
o ns. e complete formulaas are a trivial exuse generating the figures.
e t ank F. Sciulli for raising thiiss possibility.
Z x„xb,Q')= '—, g I [fq'(x„g )f'' xb, 
quark
flavors q
+f + (x Q2)f (b)(x Q2)]
X(L,q+Rq)I . (4.40)
The neutral current couplings I.& and R have be
(416) Th i tg tdZ cross section is
G~rrr I dxZ(x, r/x, M )
~zo= 2
G~m.
=3~2 & 2
qq (g 2+ ~ 2)
dW„„dW
=3.3 nb 0.59m +0.75~
dr ' dr (4.41)
I x I, , ~ I'~ ' I
~gC~h
C0
20 60
0
I
40
II
80 i00
FIG. 1
~s (Tev) . Cross sections for 8'+—production in
th D IIY i t Al h
+ ure. so shown are the cr
e rapi ity interval —1.5 &
of parton distributions was used
Rev. Mod. Ph s. V
~ . y ., ol. 56, No. 4, October 1984


Eichten et BI.: Supercollider physics 623
Integrated cross sections for Z production in pp and
pp collisions are shown in Fig. 115 for the distributions of
Set 2 and in Fig. 116 for those of Set 1. Again the cross
section if the Z is restricted to rapidity between + 1.5
and —1.5 is also shown. The pp cross section is larger by
a factor of 5 at Ms =0.54 TeV, but the advantage of pp
over pp diminishes rapidly with increasing energy. It is
only a 15% effect at v s = 10 TeV. The rapidity distribu
tions are similar to those anticipated for W-+ production.
The transverse momentum of the W's and Z's produced in the processes discussed so far is small. There are higher-order QCD processes which can produce a W (or Z) with large transverse momentum (pz }, the p~ being
balanced by a hadronic jet. The processes g +q~8 +q
and. q+q —+8'+g are shown in Fig. 117. The cross sec
tions are given by Halzen and Scott (1978). The cross sec
tion for producing a W+ with rapidity y is given by
da & f '(x„Q )f~ '(xb, Q )&;,(s,t, u)
dpi' de&; +min x~s +u —Mp (4.42)
where
with
t = —vs mme «+Mw
u = —Vsmte +M 2w,
S =Xgxys
2
t= —"v SxaNlle +~K ~
u = —t/sxbmte +Mw
22 2
ml — —Pl+My,
—x, t —(1—xu )Mw2
Xb =
xmas +Q —Mg
xm;„= — /u(s +t —Mw },
(4.43)
(4.44)
We have used Q =pi in generating Fig. 118, which
shows do'/dpgdJ7 ~ & p as a function of pj for various en
ergies. For a recent thorough treatment, with specific applications to SppS experiments, see Altarelli et al. (1984).
The number of intermediate bosons produced at a high
luminosity supercollider is impressively large. At a c.m. energy of 40 TeV, for example, a run with an integrated luminosity of 10 cm would yield approximately
6X 10 Z 's and 2X 10 8'+—'s. For comparison, in a high
luminosity Z factory such as the Large Electron
Positron Collider (LEP) at CERN (W =2 X 103'
cm 2sec ') the number of Z 's expected in a year of
running is approximately 10 . While I,EP is expected to operate at least five years before a multi-TeV hadron collider, there are conceivably some advantages in the high
02
(4.45)
and the partonic cross-sections are for q +q ~ W+g
2n.aa, (Q ) (t Mw) +(O' Mw—)—,
&gg(s, t, u ) = 9Xg stu b 10
p p ~ Qf + anything
vs = 40 TeV
and for q+g~W+q or q+g~W+q
maa, (Qz) s z+6'z+2Mwr
&(s,t, u ) = +(r~u) .
12xg (4.46)
~QC~i
D
r
/ /
/r
:TI / ~/
1 I I ~ I~
lyl & 1.5
—1
10 -6
v0
'IH -0. 1 —0. 2
I
Ki 0 Q
Set 2
O. . ICoL
Set 2
40 BO
(Tev} e0 100
-0. 4 —0. 5 —0. 6 —0. 7 -0. 8 —0. 9
FIG. 111. Cross section for W+ production in pp collisions
evaluated using the parton distributions of Set 2. The 8' cross sections are equal. Also shown are the cross sections for
8'+ produced in the rapidity interval —1.5 &y & 1.5.
0y 2
FIG. 112. (a) Rapidity distribution for W produced in pp col
lisions at ~s =40 TeV; (h) the net helicity of the W'+ is a func
tion of rapidity. Parton distributions of Set 2 were used.
Rev. Mod. Phys. , Vol. 56, No. 4, October )984


624 Eichten et a/. : Supercollider physics
100 20 5
I III I I~
50 10
2 1 0.5 mrad
0.25 2
10
60 30 10
I II I I I I I II I I f I
90 45 15 5
0
~1 II I
i II
1 0.5 0.2 68 g QC)
C0
I i i i& I i i Ii Ir
I I I 1 I I I II I I
10
20 70
I I l I I I II
I I I I I I g I &max
0.54 2 5 10 40 100
I y + 10
N
FICz. 113. Correspondence of angles to the c.m. rapidity scale used in other figures. Also shown is the maximum rapidity,
y,„=ln{V s /M~„„„)accessible for light secondaries. 20 40
Set 2
60
II
80 (TeV)
2
10
p p ~ ~ + anything
~s = 40 TeV
10
10-1 -8
et 2
02
y
o
I
(b) 0. 6
04
—0. 2 —0. 4 -0. 6 -0. 8
-6t I
0y 2
FIG. 114. (a) Rapidity distribution for 8'+ produced in pp col
lisions at V s =40 TeV; (b) the net helicity of the produced W+
as a function of rapidity. For 8' production replace y~ —y.
Parton distributions of Set 2 were used.
energy kinematics for some special purposes. This is an issue that deserves further study in the context of specific detectors and physics goals. In the case of charged intermediate bosons, there is no comparable source in prospect, but again there the question of how and why to study W decays in various regions of phase space must be examined in detail. The physics interest of rare decays of
W +—and Z has been considered by Axelrod (1982). Fur
ther discussion of the decays of W and Z into exotic modes will be given in Sec. VI.
The signature for W and Z will now be discussed brief
ly. The decay Z —+e+e or p+p each with a 3% branching ratio should produce a clear signal with essen
FIG. 115. Cross sections for Z production in pp {dotted line)
and pp (dashed line) collisions evaluated using Set 2 of distribu
tions. Also shown are the cross sections for Z produced. in the
rapidity interval —1.5&y&1.5: pp (solid line); pp (dotted
dashed line).
tially no background apart from instrumental problems, such as e/m. separation. The leptonic decay W~ve, vp
will enable the W momentum to be reconstructed if the missing transverse momentum in the event (carried off by the neutrino) can be measured. This method cannot be used clearly in events with other sources of missing pz,
such as a 8'pair event where both 8"s decay leptonically. An important question is whether one can identify
8'~qq by looking at hadronic jets. For low-momentum
8"s where the opening angle between the jets is large this method may be applicable. One would hope to see a peak in the jet pair mass. The background is, of course, from multijet QCD events, which are difficult to estimate reli
ably (see Sec. III). For a high-momentum W the two jets will be close together and may not be clearly distinguished and one may have to measure the invariant mass of a sin
gle jet. The relevant background is now a single QCD jet
with large invariant mass (M). For a jet of energy E, the
distribution in /=M!E is given roughly by dN/dg
=0.25e ~ (Paige, 1984), as predicted by the ISAJET Monte Carlo (Paige and Protopopescu, 1981), using our
Set 1 of distributions. The formula is applicable for
E =5 TeV, but the dependence on E is rather weak. The
distribution is rather broad and the average value of M is
of order 0.15E. This background is potentially serious and a more detailed study is needed. En any case it seems
that it will be difficult to distinguish W and Z from their hadronic decays, but such a separation would be extremely useful.
C. Pair production of gauge bosons
Incisive tests of the structure of the electroweak interactions may be achieved in detailed measurements of
7%'e are grateful to Frank Paige, M. Shochet, and Pierre Darriulat for a discussion of these issues.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


10
C2
en et al. : Supercoil~der physics
iD -1
625
C
a+ 10
N
io-8
VLV0
J3
H 1Q
'CmQ LLl 10-4
ng
Set 1
1
20
II
80 (TeV)
40 60 100
FIG. 116
ton distributions. Also h
using Set 1 of the par
duced in the rapidit i
s. so s own are the cross 0
pi i y interval —1.5& 1
sections for Z pro
do dd hd
the cross sections foorr prroduction of W+W, W~Z
, W-y, and Zy pairs. The rate for
tioni sm it toth ate boson. In h
e magnetic moomment of the intermedi
n t e standard model th cancellations in the
e here are important
production which
in t e amplitudes for W+ w ic rely on the au e s
O' 8' and 8'+—Z
and Z y reactions
ri inear couplin s in t"
g
si ive to nonstandard in
might arise if th
interactions such as po
e gauge bosons wer
and Z Z final states ma ant b k o d to th d
d o 'bl d
o e etection of heav egrees o reedom (see Sec. VI).
10-6 100
-v 1D 0.4
Production of W+W——pairs
The Feynman diagrams for the process
q q ~8'+8' (4.47)
are shown in Fi . 119.
'g. . The intrinsic intere st in thcs pro
0. 8
l
1.8 2 8.4
FIG. 118. Differ
p, (Tev/c)
erential cross section da/d pj. 4' I y=o
as a function of th
v
j, a s=2, 10, 20, 40 70, and 100 TeV. Set 2
FIG. 117. Lowest-order Feynman gra hs f
q~ +q.
I q,l
FIG. 119. owest-order Feynmmaann diiaagrraamms for the reaction irect-channel Hi s ishes be aus thee quarrk s are idealized as massless.
Rev. Mod. Ph ys.., Vol. 56, No. 4, October 19S4


626 Eichten et a/. : Supercollider physics
cess, which accounts in part for plans to study e+e an
nihilations at c.m. energies around 180 GeV at I EP, is
owed to the sensitivity of the cross section to the interplay
among the y-, Z -, and quark-exchange contributions.
As is well known, in the absence of the Z -exchange term, t'he cross section for production of a pair of longitudinally polarized intermediate bosons is proportional to s,
in gross violation of unitarity. It is important to verify
that the. amplitude is damped as expected. Whether this
direct measurement or the study of quantities sensitive to electroweak radiative corrections ultimately provides the
best probe of the gauge structure of the interactions cannot be foretold with certainty. The differential cross section for the elementary process
(4 47) (Brown and Mikaelian, 1979), averaged over quark
colors, is conveniently written as
( W+W )=
dz 2 "t
ap.s
24x ~$
4
ut —Mp
sA.2 3
r
s —6M~
s —Mz
Ls s
T3i(1 xs'r) s —Mz
+- 2
12M' L. +.R.
Az 4(1 )2
Mz
s —Mz
+L3|l
MzsPg L; +Ri
+ (s —Mz2) 1 —x w
Mz I;
+8( —e;) 2 1+ s —Mz &3s
42
g t —Mg 2Mn ' +
st
4
ut —Mg
~t
Mz Ls.
+e(e;) 2 1+ s„—Mz
ut —Mg4
$Q
2M@ +
Q
ut —Mg4
(4.48)
where again t (u) measures the momentum transfer be
tween q; and W ( W+), e; is the electric charge of q;,
and
x. and xb by
yb „=—,ln(x. /x, ) . (4.51)
Pg ——(1—4M@ /s)'i (4.49) The rapidity of the product in the parton-parton c.m.
frame is simply
x =&boos~+a (4.50)
where yb, is related to the parton momentum fractions
l
In order to impose experimental cuts on the produced
W s, it is convenient to decompose the rapidity of a prod
uct in the hadron-hadron c.m. frame in terms of the rapi
dity y~ of the product in the parton-parton c.m. frame
and the motion of the parton-parton system with respect
to the overall c.m. , as characterized by yb
y~=tanh '(pz), (4.52)
where z =cos8~ measures the c.m. scattering angle and
' P=(1 4M'/s—)'i (4.53)
The cross section to produce a W+ W pair of invari
ant mass M =Vs~ such that both intermediate bosons lie
in the rapidity interval ( —Y, Y) is then
(ab~ W'+ W +anything) = g dyb „[f '(x„Mz)f;.' (x&,Mz)+ f;."(x„M2)f"'(xb,M2)]
dM s . —Y
l
ZQ
&& f dz (qiqi~ W+W ), (4.54)
where as usual
x =V~e'
(3.27)
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


do' ps dz
Eichten et al.~ .: Supercollider physics 627
The limit of the an ula ~~~~g~atiOn jS give„b
min [P tanh( & &b sI), 1] .
The result of tti.,-e angular integration is
(4.ss)
(4.56)
2
7T&
12x& ~ 4 pw 0(1—&0/3) 3
xmas
s —6M~2
s —M2z
$
r3I(1 —xw) s — z
2 12M~
8'+ s
L +Z,.'
4(1 —x w)'
p Mzspiw I ~~I z
(s=Mz2)2 1 —xw A.
z 3l
s —M
M
~ TM&3 z; + — ~TMw+2sl)n(t /t )]
t++t ln(t~ /t
s
t+ —t
where
+zo ) =Mw —T~s( 1 +Pwzo ) . (4.58)
The rate of W+W
~~ ~
pair production in
isions is presented in F'
e in igs. 120 and 121
' n pp and pp col
t e total yields as well h
, where we show
we as the cross section ymg rapidity cuts of ~
o 1 li1c o i ' 0
s o y &1.5 or 2.5. I
o impose instrumental
d md . H owever, at the ener ies
gul r cov rage do to a e capture essentiall all t di b
'a e oson with (y ~ &2.5.
Mw(t+ —t" )
st+t ' (4.s7)
The yield of ~+ @
energies. F p s quite substantial. at h h
~
~
~
~
~
~
~
or example a run with
ig wi mtegrated luminosity cm would result in pp o e ey to exploiting this oten h
' g e intermediate bosons r
d, hih
0 greater interest b th f
cancellations and for h
o or the verifi cation of gauge
go
or t e assessment of b
p
son ecays is the m is is shown for in
collisions. The
in Figs. 122 aannd 124 for pp and
e mass spectrum for ~ +
od d th h
of th 11
a ig energies seems ade
1
ce a ions, provided that the interm d'
sons rov ' erme iate
III
10
lyi 2.5
b 10
lyl C 2.5
10 10
10 10
10 0 20 40 60
II I
80 100
th rto d' trib t' f
'd t t d t d.
Set 2
60
10 I I I I
0
I
20 40
II II
80 100
(T )
h d b f pairs in colli '
u ions o Set 2. Both W's pidity cuts indicated.
s must satisfy the ra
Rev. Mod. Phys. , Vol. 56 N
~, . , o. 4, October 1984


628 Eichten et a/. : Supercollider physics
10-2
)VI 10
C
WW .5
—3
io
V.
0
0 10-4
C
10-5
'U io-5
'O
10-e
10-7 10
10-8 0.4 0. 8 i.e
Moss (Tey/c )
10 0.4 1.2 2.4
Mass (Tey/c')
FIG. 122. Mass spectrum of 8'+8' pairs produced in pp col
lisions, according to the parton distributions of Set 2. Both 8'+ and W must satisfy ~y ~ &2.5.
FIG. 124. Mass spectrum of 8'+ 8' pairs produced in pp col
lisions, according to the parton distributions of Set 2. Both 8'+ and W must satisfy ~y ~ &2.5.
bosons can be detected. We shall discuss the signal-tonoise ratio for heavy Higgs decays in Sec. IV.D below. In
models in which the interactions among 8' bosons become strong, the scale of interest is an invariant mass of
around 1 TeV/c . In the standard model we anticipate a few hundred events in a 10-GeV/c bin around 1 TeV/c
at a c.m. energy of 40 TeV. The yield could be enhanced
by an order of magnitude if nonstandard interactions are present (Robinett, 1983b). An example of a factor of 2 enhancement will be given in our discussion of tech
nicolor models in Sec. VI.B.
—2
10 2. Production of W+—Z pairs
O) —3
Q 10
(3
C
10
"0 b
io-5
10-e
I
W The Feynman diagrams for the process
q;qj ~ 8' +—Z (4.59)
are shown in Fig. 125. This process is also of interest as a probe of the gauge structure of the electroweak interactions. The differential cross section for reaction (4.59) (Brown, Sahdev, and Mikaelian, 1979), averaged over quark colors, is given by
10-7
io 0.4 0.8 Moss (Tey/cQ
q
I
FICx. 123. Mass spectrum of 8'+8' pairs produced in pp col
lisions, according to the parton distributions of Set 2. Both 8'+
and W must satisfy ~y ~ &1.5.
FICx. 125. Lowest-order Feynman diagrams for the reaction
q;qj. —+8' —Z .
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et af.: Supercollider physics 629
do'
df
ma JUJ[z 6$ x~
1
s —Mg
9 —8 2 2
4 (u t M—wMz )+ (8xw 6 )—s(Mw+Mz )
u t M—wMz~ s (—Mw+Mz~ )
+ s —M~
(u t Mw—Mz) L,. L,z s (Mw+M') L.L.
+ '+'+
xw) t u 2(1 —xw) t u (4.60)
The cross section to Produce a W —Z pair of invariant mass M = v s~ such that both intermediate bosons lie in the
Y
(ttb~ W +—Z +anything) = g dy~ &[f,. (x„~~)f'.t'(x ~&)+f~ ~(x ~&)f)b~(x ~2)]
dM EJ
Zp P7+Z (4.61)
where x, and xs are given by (4.54) and
der ps do. dz 2
where in this case
(4.62)
Mw +Mz
1— s
1/2
4M' Mz
s (4;63)
The result of the angular integration is
'o do ma p zo (9 —8xw)P (1 —zo/3)
dz + (4xw —3)E'
—'o dz 6x ws 4(1 —Mw/s ) 4
(E'/2+MwMz'Is ')
+2(1 —xw) )L, —zo(1 —e'/2)
L; +LJ (1 s'/2) 4MwMzzo L;LJ.c.' )L
4(1 —xw) P s [(1—e'/2) —P zz] (1 —xw)P(1 —e /2) (4.64)
where
s'=(Mw'+Mz')/s,
and
1 —s'+Pzo
jL=ln 1 —s' —Pzo
with
zo =min[Pw tanh( F —yb „),1 ]
Mg —Mz
22
1+ s
(4.65)
(4.66)
(4.67)
I
The rate of 8'+Z and 8' Z pair production in pp
and pp collisions is presented in Figs. 126 and 127, where we show the total yields as well as the cross sections for intermediate bosons satisfying rapidity cuts of ~y ~ & 1.5
or 2.5. The yield of 8'Z pairs is approximately a factor
of 5 smaller, for each charge, than the W+W yield shown in Figs. 120 and 121.
The mass spectrum of W —Z pairs in pp collisions is
shown in Figs. 128 and 129 for gauge bosons satisfying
the cuts ~y ( &2.5 and (y ~ &1.5. Here we expect, in a
run with integrated luminosity Jdt W = 10 cm
about a hundred events per 10-GeV/c bin in the interesting region around 1 TeV.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al.: Supercollider physics
b 10
—2
10
pp ZW +ZW
lyl C 2.5
10-3
ee0
VLI 10
c
9' ~ Zw +Zw
10
—4
10 0 100
40
fI I1
20 60 80 (T~V)
FICr. 126. Yield of 8' +
d Z pairs in pp collisions, according to
the parton distributions of Set 2. Both intermediate bosons must satisfy the rapidity cuts indicated.
3. Production of Z Zo pairs
The Feynman diagrams for the process
q, q;~Z'Z' (4.68)
0. 8
10-8 I I I I I
0.4 1.2 8 8.4 2. S Mass (TeV/e*)
FIG. 1228. Mass spectrum of 8' —Z pairs produced in pp col
+
isions, according to the parton distributions of Set 2. Both S'and Z must satisfy ~ y ~ & 2. 5.
r
I1
—Mz t u (4.69)
are shown in Fig. 130. This process is of interest as a
background to the production and decay of heavy Higgs bosons, and as a channel in which to search for unorthodox interactions. The differential cross section for reaction (4.68) (Brown and Mikaelian, 1979) may be written in the form
vru (I.; +Rg )
dt 96x~(l —x ) s
4Mz
.X —+ ~+
u t tu
-3
~
10 NV
0
10
c .~ lyl 4 2.5
where we have averaged over the initial quark colors and
included a statistical factor of —' , for the identical particles in the final state. The cross section for production of Z Z
a pa1r o I
variant mass M =v sv such that both intermediate bo
sons lie in the rapidity interval ( —F, Y) is
10 lyl & 2.5 10-e
10
10-7
10 0 100
40
II II I
20 60 80
ie o Z pairs in pp collisions, according to
the parton distributions of Set 2. Both interm'ediate bosons must satisfy the rapidity cuts indicated. The W Z yield is identical.
0. 8 1.8
10-8 I I I I
' I I ~I
0. 4 2 2.4 2.. 8
Mass (TeV/e*) FIG. 129. Mass spectrum of 8'+Z pairs produced in pp col
0
isions, according to the parton distributions of Set 2. Both S'+
and Zo must satisfy ~y ~ &2.5. The W Z yield is identical
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984


c ten et al.: Supercoiiider physics
&~ (ab~Z Z +anything) — y
s r yboost] fi (x~ &~ )f. ~(x-~&)+f(0)( ~Q (b)
b» i xa ~; (xb,~z)]
0 dCT
X dz (q,.q,.~Zozo)
where
631
(4.70)
with
Ps" dg dz 2 d"t
P=(1 —4M'/s )'~z
n.a p
48x~(1 —x ) s
4+ ez 1 —e/2+ pzo
2P(2 —s) 1 e/ 2— Pzo
s +2P (1 —zo)
0 e +4P (1—zo)
The integrated cross section is
f
&& d dcT
0d
(4.71)
(4.72)
(4.73)
~dt =10 cm are approximately 2X 105 Z with ~y ~ &2 5
prerequisite to detai]. ed st d
tlon e iclency is a
The mass spectrum of Zozo
shown in Figs 133 d 134 f Pp co lisions is
these spectra in our d ' . . s all return to
discussion of the observab 1 t
" vy»ggsbosonslnSec $VD F
that in the stand d d o, et us remark 10-G V/ b
pect about 50 events in a
n ar model we ex
e c » around 1 Tey c
un with integrated luminosity of 1()
+
4. VV-y production
where as usual
zo=min[p 'tanh(T —yb „),1],
e=4mzz/s . (4.74) is
(4.75)
The elementa r
ry p ocess which operates in the reaction ++
p —p ~ 8' —y+ anything
The rate of Z Z ppaaiir production in
lisions is present d F
e in igs. 131 and 132 w the total yie1ds as well as
, where we show s as we as the cross sections for inte ate bosons satisfying the rapidity cuts —1o
pairs is smaller b a
o W pairs. At Vs =40 TeV and for
(4.76)
ee
for which the Feynman dia ram
Th d'ff
e i erential cross section has been cal v, an ikaelian (1979) and Mika Samuel, and Sahdev (1979). The resu t tial quark colors is
e result, averaged over ini
(q;qj ~ W+—y) = s &w
t~+u ~+2M s
1+t/u (4.77)
wher " ' e (Kobayashi and Maskawa
where UJ is an element of the
quar mixing matrix and t
turn transfer between q; and W . The s
n t measures the momen
ho ld fo W+ od
y pro uction, with t heinie ret
bt
er etween q and W+. Th e invariant
y pair is given by sr The vanishin. g of
b 10
10
10
I
q
II
FIG. 130. Lowest-order Feynman dia
q;q; ~z'Z'. an iagrams for the reaction
10 0 100
40
II1It 1
80 60
II
80
FIG. 131. Yield of Z Z pairs in colli '
parton di t 'b
is rs utions of Set 2. Both interm
pp collisions, according to the
satisf th 'd'
y e rapi sty cuts indicated.
o intermediate bosons must
Rev. Mod. Ph ys. , Vol. 56, No. 4, October 1984


Eichten et a/. : Supercollider physics
10-3
1-0-1
10
lyl 2.5
O
9 10-4
CC)
l & 1.5
10-5
D
10 0 20 40 60 80
~s (Tev)
100
FIG. 132. Yield of Z Z pairs in pp collisions, according to the
parton distributions of Set 2. Both intermediate bosons must satisfy the rapidity cuts indicated.
-3
~10
oe0
VL 10
C 2.5
the differential cross section at t/u =2 (which corre
sponds to cos8, = ——, ) has been understood (Brodsky and Brown. , 1982; Samuel, 1983; Brown, Kowalski, and
Brodsky, 1983) in terms of classical radiation zeroes. The total rate observable in experiments depends sensi
tively upon the 8'y invariant mass and consequently on the minimum detectable energy of a photon. Figure 136
shows the total cross section for pp~W +—y when the in
variant mass of the 8' and the photon is restricted to be more than 200 GeV/c . This cut removes the infrared divergence when the photon energy vanishes. The cross
sections are constrained so that both the 8' and the pho
ton have rapidity between + 2.5 and —2.5. A tighter ra
10-8 0.4 0.8 1.2
I I'. I 1.6 2 2.4 2.8
Mass (TeV/c') FIG. 134.. Mass spectrum of Z Z pairs produced in pp col
lisions, according to the parton distributions of Set 2. Both Z 's must satisfy ~y ~ & 1.5.
pidity cut of y & ~ 1.5 ~ is also shown. The total cross
section is, of course, formally infinite, since the expression (4.77) has a t channel pole. Figure 137 shows the distri
bution in cos8, at v s =40 TeV, where 8 is the angle be
tween the photon and the beam in the 8'y center of mass frame. We have applied a cut on the transverse momentum of the photon of 20, 50, and 100 GeV/c. The distri
bution is sensitive to the details of the 8'8'y coupling
and in particular to the magnetic moment of the S'. Departures can be expected in nonstandard models such as composite gauge boson theories (Robinett, 1983a).
'0 b 10-5
5. Z'y production
The Feynman diagrams for the process
Sqs~Z 'V (4.78)
10
10-7
are shown in Fig. 138. This process is chiefly of interest as a channel in which to search for unorthodox interac
tions. For example, I.curer, Harari, and Barbieri (1984)
have shown that in a composite Z scheme the process
q+q~Z +y may yield large pj photons at a rate sub
stantially greater than predicted by the standard model. In the standard model, the differential cross section for reaction (4.76) is (Renard, 1982) 0.4 0.8 1.2 1.6 2.4 2. 8
Maes (TeV/c ) (q;q; —+z y)=
dt
n.a (L;+R; ) s +Mz
6xp (1 —xg )s Zt u
FIG. 133. Mass spectrum of Z Z pairs produced in pp col
lisions, according to the parton distributions of Set 2. Both Z 's must satisfy ~y ~ &2.5.
(4.79)
where we have averaged over the initial quark colors.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et aI.: Supercollider physics
Cf
FICx. 135. Lowest-order Feynman diagrams for the reaction q;qJ~R' +—y.
Figure 139 shows the total cross section in pp collisions
where we have required that the Z and photon have in
variant mass of more than 200 GeV/c, and that they
satisfy rapidity cuts of ~y ( &2.5 and (y ( &1.5. Figure
140 shows the distribution in cos8 at Vs =40 TeV (see preceding section); again the transverse momentum of the photon is restricted to be greater than 20, 50, and 100 GeV/c.
D. Production of Higgs bosons
G MX
I (H~ff)= (1 4mf—/Mlr) ~
4' 2 (4.81)
where N, is the number of fermion colors. For MIr
& 2M~, the preferred decay of the Higgs boson is into the
heaviest accessible pair of quarks or leptons. In contrast, a Higgs boson with MH &2M~ has the
striking property that it will decay into pairs of gauge bosons. For the intermediate boson decay modes, the partial widths are given in perturbation theory by (Lee, Quigg, and Thacker, 1977)
In the standard electroweak theory, a single neutral scalar particle remains as a vestige of the spontaneous break
down of the SU(2)L U(1)r gauge symmetry. As we have
already noted in Sec. I.B, the mass of this Higgs boson is not specified by the theory, but consistency arguments suggest (Linde, 1976; Weinberg, 1976a; Veltman, 1977; Lee, Quigg, and Thacker, 1977)
6M
1(H Z Z )= (4—4a +3az)(l —az)'
64m' 2
(4.82)
(4.83)
GM
I (H~R +W )= (4 —4agr+3a~)(1 —aii )'~
327r 2
7 GeV/c &MH &1 TeV/c (4.80)
The interactions of the Higgs boson are of course prescribed by the gauge symmetry. It is therefore straightforward to write down the partial widths for kinematically allowed decays. The partial width for decay into a fermion-antifermion pair is
—1
10
C
~s 40 TeV
DC
—1
10
PP — = yYV +yW
'+i0ON0
'Qb 10
10 ~yI & 2.5
—4
10
lyl ( 1.5
—3
10
5
10 0 20
—0. 4 casO
0. 4
~s (Tev)
FIG. 136. Total cross section for the reaction
pp ~ 8'+—y+ anything as a function of V s. The invariant mass
of the 8' +—y pair is more than 200 GeV/c: Both W +—and y
must satisfy ~y ~ & 1.5 or ~y ~ &2.5, as indicated. Set 2 of the distributions was used.
FIG. 137. Distribution in cos8, where 0 is the angle between
the photon and the beam in the 8'y c.m. frame, for the process
pp —+ W+—y+ anything at V s =40 TeV. The transverse momen
turn of the photon is restricted to be greater than 20 (dashed line), 50 (dotted-dashed line), or 100 (dotted line) CxeV/c. Set 2
of the distributions was used.
Rev. Mod. Phys. , Vot. 56, No. 4, October 1984


634 Eichten et al. : Supercollider physics
—1
10 ~y& C 2.5
tyl C 1.5
FIG. 138. Lowest-order Feynman diagrams for the reaction
q;q; ~yz'.
where as 4M'—/—MH and az — —4Mz/Mtt. The resulting
partial decay widths are shown in Fig. 141. There we also
show the partial widths for the decay H~QQ for heavy
quark masses of 30 and 70 GeV/e . The decay into pairs
of intermediate bosons is dominant. If the perturbatively estimated width can be trusted, it will be difficult to establish a Higgs boson heavier than about 600 GeV/c .
The expected properties of light Higgs bosons have been reviewed by Ellis, Gaillard, and Nanopoulos (1976), and by Vainshtein, Zakharov, anti Shifman (1980). The
heavy Higgs alternative has been explored by I.ee, Quigg, and Thacker (1977), and by Gordon et al. (1982). A number of production mechanisms for Higgs bosons has been considered. Here we discuss the production of Higgs bosons in isolation; associated production of Higgs bosons and intermediate bosons will be treated in Sec. IV.E. The direct production of a Higgs boson in the reaction
(4.84)
—3
10
—4
10
10-5 80 40 60
I1
80 v s (Tev)
100
FIG. 139. Total cross section for the reaction
pp~Zy + anything as a function of V s. The invariant mass
of the Zy pair is more than 200 GeV/c . Both the Z and y
must satisfy ~y ~ &1.5 or ~y ~ &2.5, as indicated. Set 2 of the distributions was used.
For light quarks this is negligibly small even for rather
light Higgs bosons because of the (I; /Mtt) factor. For
heavy quarks this contribution is small because of the small parton luminosity. Figure 143 shows the Higgs
production cross section' via this mechanism for m, =30
GeV/c as a function of Mtt. The pp and pp rates are
equal. In particular, the cross section due to the reaction
tt~H for MIt ——100 GeV/c and m, =30 GeV/c is
only 9 pb at v s =40 TeV. A more promising source of Higgs bosons in hadron
is depicted in Fig. 142. The differential cross section for the reaction PP yZ
a +b~H +anything
is given by
(4.85) —1
10
XCl ~s = 40 TeV
2
dy 3 2; MH r[f (x„MH )f';'(xb, MIt ).
+f;."(x„MJ)f; '(xb, Mtt )],
os
NO0
—z
10
(4.86)
where r=Mttls and x, b are given by (4.10). The integrated cross section is then given by
MH
Nl)
=3.36 nb+ MH
Gym.
o (ab ~H+ anything) = 3 2
(4.87)
10
eose 0. 4 0. 0
SA11 our production cross sections are given in zero-width approximation for the Higgs boson. This approximation will underestimate the production rate when the Higgs width becomes very large.
FIG. 140. Distribution in cos8, where 0 is the angle between the photon and the beam in the Zy c.m. frame, for the process
pp~Zy + anything at V s =40 TeV. The transverse momen
tum of the photon is restricted to be greater than 20 (dashed line), 50 (dotted-dashed line), or 100 (dotted line) GeV/c. Set 2 of the distributions was used.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 635
IOOO f
M~=82 GeV/c M =95 2
Z
~ IOO
50
20
10-1
CQl
Co
T. 10-3
CL 4
10
b
io -5
qq fusion
10-8
—7
10 I I I
100 200 500 M„(GeV/c )
IOOO
FIG. 141. Partial decay widths of the Higgs boson into inter
mediate boson pairs vs the Higgs-boson mass. For this illustra
tion we have taken M~ ——82 GeV/c and Mz ——93 GeV/c .
0. 8 0.8 1.4 1.8 Mass (Tsv/e~)
FICx. 143. Total cross section for Higgs boson production by qq
fusion in pp collisions as a function of the Higgs boson mass at
Vs =2, 10, 20, 40, 70, and 100 TeV, according to the parton distributions of Set 2.
collisions is the gluon fusion mechanism indicated in Fig. 144 (Creorgi et al. , 1978). This process makes a contribu
tion to the differential cross section for Higgs production 0
Consequently the integrated cross section is
2
Gp.n a,
rJ( ab ~H +anything ) = 32 2
(4.90)
dc' G~m a,
(ab ~H +anything) =
dp 32 2 7r
2 A quark with m; &MB gives q= —,. For 4m; &MH, q is complex. Defining
Xfs' (x„M~)fg '(xb, MH), s=4m; /M&,
we may write
(4.91)
where (Resnick, Sundaresan, and Watson, 1973)
(4.88) rl = —[1+(E—1)y(e)],
2 (4.92)
dy(1 —4xy)
o o 1 —(xyMIt /m; ) (4.89)
and the strong coupling constant is evaluated at MH.
with
—[sin '(1/V s)], s & 1
q(s) = ', [1 (gn/+g —)+i~],e(1, (4.93)
l
FICr. 142. Feynman diagram for the production of a Higgs boson in qq collisions.
FICx. 144. Feynman diagram for the production of a Higgs boson in gluon-gluon fusion.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


636 Eichten et af.: Supercollider physics
where 0.5
/+=1+@'1—e . (4.94) 0.4
We plot ~ rl(s) ~ as a function of E in Fig. 145. For quark masses m; &70 GeV/c and Higgs boson masses
mH &200 GeV/c the parameter c is less than 0.5. In this region ~ g(e. ) ~ may be approximated by
0.3
0.2
i g(e) i =0.7s, E&0.5 . (4.95) Q. I
Consequently the production rate from this mechanism is proportional to m; and light quarks are ineffective. The total cross sections for Higgs boson production by this gluon fusion process are shown in Fig. 146 for
m, =30 GeV/c and in Fig. 147 for m, =70 GeV/c .
The sensitivity to the top quark mass is apparent. Dif
ferential cross sections for Vs =40 TeV are plotted in Fig. 148. They show the expected behavior, with light Higgs bosons produced uniformly in rapidity and heavy
Higgs bosons produced more centrally. The number of events is not large. In the case of the ZZ final state, the
requirement that both Z's decay leptonically will result in
only nine events for mII -500 GeV/c and m, = 30
GeV/c at Vs =40 TeV and for f ddt=10 cm
This small number of events may be sufficient in the absence of background (see below).
& =4m.2 /M 2
iH
FIG. 145. Function ~ g(e) ~ defined in Eqs. (4.93) and (4.94).
Another mechanism for the production of heavy Higgs bosons earlier discussed by Petcov and Jones (1979) has recently been studied by Cahn and Dawson (19.84). This is the intermediate boson fusion mechanism depicted in Fig. 149, which becomes important at large Higgs boson
masses, because the coupling of the Higgs boson to longi
tudinal W's and Z's is pi'oportional to MH. Useful approximate forms for the cross sections are (Chanowitz and Gaillard, 1984; Cahn and Dawson, 1984)
1 cx
~$yttH(ab~H +anything) = 16M~
3
[(1+M~Is )in(s/M~) 2+2M~—Is]
& yf (x MH)fk (xb MH)@ efek)
i, k
(4.96)
and
3
ozzH(ah~H+anything) = [(1+M~/s )ln(s /MH ) 2+ 2MII /s ]
64Mpr x$f'(1 x~)
&& + [(L)~+R; )(Lk+Rk)f)"(xg)MH)fk '(xb)MH )] . (4.97)
i, k
These approximations assume that the gauge bosons are emitted at zero angle. The total cross sections for Higgs boson production by intermediate boson fusion are shown in Fig. 150. This contribution exceeds that from gluon
fusion for Higgs boson masses in excess of about 300
GeV/c if m, =30 GeV/c, as may be seen by compar
ison with Fig. 146. For a top quark mass of 70 GeV/c, the gluon fusion mechanism dominates for Higgs boson
masses up to 550 GeV/c .
To assess the observability of Higgs bosons we must
discuss the signal and the background. We will first consider the case in which the Higgs boson is heavier than
2M~ so that it decays almost exclusively into states of
W'+W or ZZ (see Fig. 141). We display in Fig. 151 the cross section for the production and decay
pp ~H +anything
(4.98)
I
at ~s =40 TeV. We have restricted the rapidity of the
that ~y~ ~ &2.5 and have assumed m, =30
GeV/c . As discussed in Sec. IV.B, this cut will ensure
that the decay products of the W's are not confused with the forward-going beam fragments. The contributions from gluon fusion [Eq. (4.90)] and gauge boson fusion [Eqs. (4.96) and (4.97)] are shown separately.
Assuming that the W's can be identified, the background comes from W pair production [Eq. (4.47)]. We
have estimated this background by taking do!dM for W pair production with ~ y~ ~ &2.5 (Fig. 122), evaluating it
at 8' pair mass M equal to MH and multiplying by the
Higgs width or 10 GeV, whichever is larger (see Fig. 141).
It can be seen that the signal exceeds the background for
M~ & 630 GeV/c . Figure 152 shows the same result for
m, =70 GeV/c . For large Higgs masses this change is unimportant, since the gluon fusion mechanism is not dominant. A tighter rapidity cut of i y~ ~ & 1.5 is shown
in Fig. 153. The effect on signal and background of a
Rev. Mod, Phys. , Vol. 56, No. 4, October 3 984


Eichten et al. : Supercollider physics 637
CQ.l
-2
cV~ «
+ —3
& 1O
10-4
Q.
b —5
10
10-2
'D0
—3
10
10-4
-5
10
—6
10 —4
I l
/ / I
I] Ij
p p ~ H + anything
4Q TeV
10-6
10-7 0.2 0.6 1.4 1.S Mass (Tev/e )
FIG. 146. Integrated cross sections for Higgs-boson production
by gluon fusion in p +—p collisions, for I, = 30 GeV/c at
Vs =2, 10, 20, 40, 70, and 100 TeV, according to Set 2 of the distributions.
10 QCl
2
c io
0
10-3
change in the beam energy can be seen by comparing Fig.
154 (V s =10 TeV) with Fig. 151. At this lower energy,
the signal and background become equal at MH ——320
GeV/c . The Higgs production rate is almost the same in pp col
FIG. 148. Differential cross sections for Higgs-boson produc
tion by gluon fusion in p+—p collisions at Vs =40 TeV. The top
quark mass is taken to'be 30 GeV/c, and the gluon distribu
tions of Set 2 are used. M~ ——100, 300, 500, 700, and 900 GeV/c 2.
lisions, but the background is larger (compare Figs. 122
and 124). At vs =40 TeV and MH ——400 GeV/c the
background is larger by approximately a factor of 4 in pp than in pp collisions.
We can also attempt to observe the Higgs in its Z-pair decay mode. The signal is less by a factor of 2 [see Eqs. (4.82) and (4.83)], but the background is less significant, as can be seen by comparing Figs. 122 and 133. Figure 155 shows the signal and background in the Z-pair final
state at ~s =40 TeV in pp collisions with ~ yz ~ & 2.5 and
m, =30 GeV/c . The signal exceeds the background for
MII &1 TeV/c . In order to estimate the reach of various machines we have adopted the following criterion to establish the existence of a Higgs boson. There must be at least 5000 events, and the signal must stand above the background by five standard deviations, The 5000 events should be
adequate even if we are restricted to the leptonic modes of
the 8"s or Z's. In particular, 18 detected events would
remain from a sample of 5000 Z pairs where both Z's de
cay into e e+ or p+p . Figure 156 shows the maximum detectable Higgs mass in the JY-pair final state,
Q 10-4
Q. b
10
10
10 I ~I I
0.2 0.6 1.4 1.6 Mass (Tev/c*)
FIG. 147. Integrated cross sections for Higgs-boson production
by gluon fusion in p+—p collisions, for m, =70 GeV/c at
~s =2, 10, 20, 40, 70, and 100 TeV, according to Set 2 of the distributions.
FIG. 149. Intermediate-boson fusion mechanism for Higgsboson formation.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


638 Eichten et al. : Supercollider physics
1
c
10-1
10
Qc 10-2
+
IVS fusia n
10-2
QQ..
& 1O
10-3
10-5 10-4
70 GeV/c*
10-B
o. e 1.4 1.8 Mass (TeY/'c')
-5 1O 0. 2 0.4 o. e O. S 1 Mass (TeV/c~)
FIG. 150. Integrated cross sections for Higgs-boson production by intermediate-boson fusion in pp collisions, according to the
parton distributions of Set 2.
10
p p P H + anything
10-2
—3
10
10-4 30 GeV/'c'
10-5 0.2 0.4 0. 6 O. B
Mass (TeV/c~)
FIG. 151. Cross section for the reaction
pp —+(H~ 8'+8' ) + anything, with m, =30 CxeV/c, accord
ing to the parton distributions of Set 2, for Vs =40 TeV. The intermediate bosons must satisfy ~ y~ ~ & 2.5. The contributions
of gluon fusion [dashed line, Eq. (4.90)] and 8'W/ZZ fusion [dotted-dashed line, Eqs. (4.96) and (4.97)] are shown separately.
Also shown (dotted line) is I do.(pp~8'+ W +X)/dM, with
~ys ~ &2.5 and M=MH, where I =max(1 H, 10 GeV). (See Fig. 122.)
FIG. 152. Cross section for the reaction
pp —+(H~ 8 + 8 ) + anything, with m, =70 GeV/c, accord
ing to the parton distributions of Set 2, for V s =40 TeV. The intermediate bosons must satisfy ~y~ ~ &2.5. The contributions
of gluon fusion [dashed line, Eq. (4.90)] and WR'/ZZ fusion [dotted-dashed line, Eqs. (4.96) and (4.97)] are shown separately.
Also shown (dotted line) is I do.(pp~8'+ 8' +X)/dM, with
~ys ~ &2.5 and M=MH, where I"=max(I H, 10 GeV). (See Fig. 122.)
/
with ~ys ~ &2.5, and m, =30 GeV/c as a function of
Ms for various integrated luminosities. The criteria applied to the ZZ final state do not yield significantly dif
ferent results. It may be possible to distinguish a 8'or a
Z from QCD jets if the 8" or Z decays hadronically. If
this is the case and one cannot distinguish between a S' and Z in their hadronic modes, then one must add the ZZ and WJF final states. In this case, the background is increased, since it receives a contribution from WZ final states (Fig. 128).
If we apply the criterion to pp collisions, we shall ob
tain results very similar to those in pp. At Vs =40 TeV
the limiting factor is the width of the Higgs as well as the production rate. An extreinely wide resonance is difficult to establish. However, as we have already remarked,
there should be sufficient W' pair events to see some
structure in the 8'+8' channel indicative of a heavy
Higgs. At V s =10 TeV the production rates are lower and a heavy Higgs is consequently more difficult to ob
serIvfe.the Higgs mass is less than 2M~, then we must at
tempt to observe its decay into a pair of t quarks,
pp +XI +anything
tt, (4.99)
for which only the gluon fusion production mechanism is important (see Figs. 146 and 150). The cross section for
Rev. Mod. Phys. , Vol. 56, No. 4, October t 984


Eichten et aI.: Supercollider physics 639
i0-1 io-1
~2 1D
pp ~ H + anything
ww
10-2
p p ~ H + anything
lyl C 2.5
10 !0-3
~~ ~~ ~ ~
iD-4 30 GeV/c~ 10
10-50.2 D. 4 0.8 O. S 1
Mess (TeV/c~)
-5 1D 0.2 0.4 0.8 0.8 Mass (TeV/c )
FIG. 153. Cross section for the reaction
pp —+(H~ W+W ) + anything, with m, =30 GeV/c, accord
ing to the parton distributions of Set 2, for V s =40 TeV. The intermediate bosons must satisfy ~ ys ~ & 1.5. The contributions
of gluon fusion [dashed line, Eq. (4.90)] and WW/ZZ fusion [dotted-dashed line, Eqs. (4.96) and (4.97)] are shown separately.
Also shown (dotted line) is I do(pp~W+ W +X)/dM, with
~yii ~ &1.5 and M=MH, where 1 =max(1 e, 10 GeV). (See
Fig. 122.)
FIG. 154. Cross section for the reaction
pp~(H~ W+8' ) + anything, with m, =30 GeV/c, accord
ing to the parton distributions of Set 2, for Vs =10 TeV. The intermediate bosons must satisfy ~ y~ ~ & 2.5. The contributions
of gluon fusion [dashed line, Eq. (4.90)] and WW/ZZ fusion [dotted-dashed line, Eqs. (4.96) and (4.97)] are shown separately.
Also shown (dotted line) is I do.(pp~W+ W +X)/dM, with
~ys ~ &2.5 and M=MH, where I =max(I e, 10 CxeV). (See
Fig. 122.)
pp ~jet~+ jet2+ anything, (4.100)
where the rapidity of each jet satisfies ~y ~ &1.5. The rate exceeds the Higgs boson production cross section by many orders of magnitude. At the other extreme, we may imagine identifying t quarks in an experimental trigger. The t-quark lifetime is estimated to be 2'5
10—19
m, (4.101)
and is consequently too short to be observed. However,
the chain t~b results in a b quark with a relatively long
lifetime (Fernandez et al., 1983; Lockyer et al., 1983),
production of a Higgs bason, with subsequent emissian of
both t and t with ~y ~ &1.5 is plotted as a function of
Higgs boson mass in Fig. 157. Although the cross sections are substantial and lead to the expectation of many events, the anticipated backgrounds make prospects for observation seem discouraging. In the absence of any highly selective topological cut, the background to this signal arises from two-jet events due to hard scattering of partons. Such events were dis
cussed in some detail in Sec. III. We showed in Figs.
90—92 the spectrum of two-jet invariant masses arising from the reaction
~(b) =(1.6+0.4+0.3) X 10 ' sec . (4.102)
A vertex detector could be used to tag this. We show in Fig. 158 the cross section for tt production via the process
gg QQ (4.103)
which is discussed at length in Sec. V. Even this background dwarfs the Higgs signal of reaction (4.99). We conclude this section with a few general comments. Our estimates of Higgs cross sections are conservative; in
particular, we have concentrated on the case m, =30
GeV/c2 and have assumed no additional generations af
quarks. If in, is larger, or if there are heavier flavors, then the Higgs production rates will increase consider
ably. We have seen that a machine with W = 10
cm 2 sec ' and v s =40 TeV should be able to establish
the existence of a Higgs if Mtt &2Mii. or will have suffi
cient event rate to be able to see structure in the 8'+ 8' channel in the event that MH is very large, provided at
least one af the intermediate bosons can be abserved in its
hadronic decay modes. If only the leptonic decays can be
observed, W = 10 cm sec ' will be required. If
MH &2M~, the discavery of a Higgs boson in p~p col
lisions seems more problematical. [For further details on
the case m, =45 CreV/c, see Eichten et al. (1984).]
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


640 Eichten et al. : Supercollider physics
pp ~ H + Qnyth&AQ
ZoZ0
Iyl 4 2.5 10
C
p p ~ H a anything
—2
io
10-3
10-3
10-4 Alt 3O GeV/c*
10
10-5 0.2 0.4 G. e 9.8 1 Moss (TeV/'c*)
10-5o. oa 0, 12 0.2 0.24 0.88
Mass (TeV/c*)
FIG. 155. Cross section for the reaction
pp~(M —+ZZ) + anything, with m, =30 GeV/c, according to
the parton distributions of Set 2, for Vs =40 TeV. The intermediate bosons must satisfy ~yz ~ &2.5. The contributions of
gluon fusion (dashed line) and ZZ/8'8' fusion (dotted-dashed line) are shown separately. Also shown (dotted line) is
I do(pp~ZZ+X)/dM with ~yz ~ &2.5 and M=M~, where
I =max(I ~, 10 GeV). {SeeFig. 133.)
FIG. 157. Cross section for the reaction
pp~(H~tt)+ anything as a function of MH with m, =30
GeV/c, according to the parton distributions of Set 2 at
V s =2, 10, 20, 40, 70, and 100 TeV. The t and t must satisfy
[y, [ &1.5.
E. Associated production of Higgs bosons and gauge bosons
In electron-positron collision, a favored reaction for Higgs boson production is
ee0
0I
C
e+e ~HZ, (4.104)
0.8
0.6
M„(TeV/c )
&0
0.2
20 60 80 loo
0I.2
0I.6 0.8
Js (TeV) FICs. 156. "Discovery limit" of MH as a function of V s in
pp~(H- —+8'+8' ) + anything for integrated luminosities of
10, 10, and 10 cm, according to the criteria explained in
the text.
Poir Moss (TeV/c )
FIG. 158. Mass spectrum of tt pairs produced in proton-proton collisions, according to the parton distributions of Set 2. The
rapidity of each produced quark is constrained to satisfy
Rev. Mod. Phys. , Vot. 56, No. 4, October 1984


Eichten et aI.: Supercollider physics 641
which proceeds by the direct-channel formation and de
cay of a virtual intermediate boson. Its advantage, in
terms of a favorable cross section, arises from the fact that the HZZ coupling is of unsuppressed semiweak strength. The corresponding elementary processes that operate in hadron collisions are
Ql 10-a
Y0c
and
qgqj —+HS'+
q;q; —+HZ .
(4.105)
(4.106)
+ 10-3
X
10-4
The cross sections, averaged over initial quark colors, are
(q;qj ~HW-) = 2
da + a' I «, I
' 2J:
48xw s
10-6
X 2 Mg+ sin 8
1 gE
(s —Mw)
and
a(L+R )
(q;qt~HZ) = 96xw(1 —xw)~ ~s
(4.107)
z+ sin
1 2E
(s —Mz)~
(4.108)
where K is the c.m. momentum of the emerging particles.
Equation (4.107) holds for W +— production when
e;+e-. =+1. The corresponding total cross sections are
10-7 0.2 1.4 1.8 Mess (TeV/c~)
FICx. 159. Integrated cross sections for associated HP' —production in pp collisions, according to the parton distributions of
Set 2.
cm . Whether this number is sufficient for discovery is a question of detection efficiency. The final state has
three gauge bosons. If all those decay hadronically this will produce six jets. A detailed Monte Carlo study is needed in order to know whether this state can be reconstructed. The event rate is so low that only one boson can probably be detected in its leptonic mode.
a(q;qJ ~ W~H) = 2Z
36xw ~s 10-1
c
and
X 2 (K +3Mw) (4.109)
(s —Mw)
m.a (L;+R; )
cr(q;q;~HZ) = 72xw(1 —xw)2 s
8
c 10
c0
10
10-4
&& 2 (X +3Mz) .
(s —Mz )
The cross sections for the reactions
p+—p ~ 8'+—H+ anything
and
p +—p —+HZ +anything
(4.110)
(4. 111)
(4.112)
CL ICL
10
10-6
«7
are shown in Figs. 159—162. Although they are significantly smaller than the cross sections for production of a single Higgs boson by gluon fusion, the annual production
rates for Mti ——400 CseV/c still run to approximately 10
HV pairs at V s =40 TeV, assuming Idt M =1040
10 0.2 0.8 1.4 1.8 Mass (T@V/c )
FIG. 160. Integrated cross sections for associated HP'+—production in pp collisions, according to the parton distributions of
Set 2.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et 8I.: Supercollider physics
—1
10
10-2
c
Dc 10-3
+
10
Q. CL
0 10
10 0.2 o. e 1.8 Moss (TeV/c~)
FIG. 161. Integrated cross sections for associated HZ production in pp collisions, according to the parton distributions of Set
2.
F. Summary
In this section we have shown how a high-energy, high-luminosity hadron-hadron collider may be exploited to extensively test the structure of the minimal model of electroweak interactions. The rate for production of W
10 Qcl
-3
0 10
MZ 4
10
lQ. 5
10
7
10 0.2 0. 8 1'. 4 1.8 Moss (TeV/c )
FIG. 162. Integrated cross sections for associated HZ production in pp collisions, according to the parton distributions of Set
2.
and Z bosons is extremely large (see Figs. 110, 111, 115, and 116). In particular, a 40-TeV collider capable of experiments with an integrated luminosity of 10 cm will
generate approximately 6& 10 8"s in a range of rapidity
( ~y~ ~ &1.5), where the decay products should be well
separated from the beam fragments. Such a large sample cannot be obtained from any other foreseeable source and provides an opportunity to study rare 8'decays. Of great importance is the detection and study of a
Higgs boson. We have shown that if M~~2M~, the
study of final states with W+ W or ZZ at v s =40 TeV should be able to reveal the presence of a Higgs boson,
provided that its mass is less than 0.8 TeV/c and provid
ed that a luminosity of 10 cm sec ' can be achieved and exploited. This requires detecting at least one inter
mediate boson in its hadronic decay modes. If both intermediate bosons must be observed in the leptonic modes, a
luminosity of 10 cm sec ' is necessary to reach above
M~ — —400 GeV/c . For a Higgs boson having a mass larger than this, the large width makes a resonance difficult to establish. In this case perturbative calculations become unreliable and the precise signals unclear. A search
for structure in the 8'+8' invariant mass distribution should reveal deviations from those predicted in Figs. 122 and 123. An example of such a structure will be given in Sec. VI. In this case luminosity and the ability to recon
struct W+ W final states efficiently are critical.
V. MINIMAL EXTENSIONS OF THE STANDARD MODEL
In this section we discuss the production rates and experimental signatures of new quarks, leptons, and intermediate bosons that may arise in straightforward generalizations of the minimal SU(2)1 U(1)r electroweak
theory for three fermion generations. The new quarks and leptons we shall consider are "sequential" replicas of the known fermions. The generalization to exotic color charges or electroweak quantum numbers is elementary, and need not be treated explicitly. Additional gauge bo
sons beyond 8 +—and Z arise in many theories based on expanded gauge groups. We shall deal with representative examples. One minimal extension of the standard model that we shall not consider here in detail is the enlargement of the Higgs sector to include more than a single complex doublet. This would imply the existence of charged physical
Higgs scalars H as well as addit—ional neutrals H '. If
the masses of these particles were less than about 40 GeV/c, the problem of producing and detecting them
would be very similar to that of the light technipions discussed in Secs. VI.C and VI.D. For neutral Higgs bosons
with M(H ') ) 2M~, the search for structure in the
8'+8' and Z Z channels, described for the conventional Higgs boson in Sec. IV.D, is appropriate. The pro
duction and detection of heavy charged Higgs bosons is more problematical. These cannot be produced in associ
ation with 8' +—or Z, because the 8' +—H ~Z coupling is
forbidden for physical Higgs scalars that belong to weak
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 643
isospin doublets. Unless the H +—coupling to light quarks
is unexpectedly large, the rate for qq '~H —will be negli
gible. The reaction gg —+H+H via a quark loop will
also occur at a tiny rate unless there are very heavy quarks in the loop. A production mechanism which does not entail small (Yukawa) couplings is the Drell-Yan process,
(5.1)
The cross section, including the contribution of the
direct-channel Z pole, is given by Eqs. (4.3)—(4.12), with the factor e; in (4.7) replaced by (Lane, 1982)
p3 2 M (M2 —Mz)(1 2xw)(L—q+Rq )
4 2xw(1 —xw)[(M —Mz) +Mzl~zl
M (1 —2xw) (Lq+Rq)
16xw(1 —xw) [(M —Mz) +MzI z]
x'
while for a new lepton doublet ( ), it is
t ML —M~ t & 1 TeV/c (5.6)
p= 1.02+0.02 . (5.8)
The difference between quark and lepton inequalities is due to color factors. Heavy-fermion loops contribute to the renormalization of low-energy observables such as
M~ GFMFX, (5.7)
Mz(1 —xw) 8m ~2
where X, is the number of colors of the heavy fermion F.
The approximate form (5.7) holds when the mass of fer
mion F is large compared to the mass of its SU(2)1 partner. A recent compilation (Marciano and Sirlin, 1983) of neutral-current cross-section measurements yields the value
(5.2) This suggests the bounds
with the chiral couplings Lq and Rq given by (4.16), and
p=(1 —4MH+/M )'i Ml &620 GeV/c' (5.9)
(5.3) for a charged sequential lepton accompanied by a massless neutrino, and
t M~ Mg) t
'~ &—350 GeV /c (5.10)
for the mass splitting within a new quark doublet. Interesting bounds in the contempt of unified theories have been derived by Cabibbo et al. (1979). The principal decays of heavy fermions will involve the
emission of a real W boson. If MU & MD [as suggested by
the (;) and (J, ) generations], we anticipate
A. Pair production of heavy quarks
Thus the cross section approaches ~ ihe lepton-pair cross section for high pair masses, modulo the differences in the neutral-current contribution to (5.2) and (4.14). Yields may be judged from Fig. 108 and Eq. (4.22). The most
prominent decay of H will be in t—o a pair of hadron jets. The signature is similar to that for the pair production of
technipions, which is addressed in Sec. VI.E.
Because we do not understand the pattern of fermion generations or masses, we must be alert to the possib1e ex
istence of new flavors. We shall analyze the case in which new quarks occur in sequential SU(2)~ doublets of color triplets, and specifically the case of quarks heavier than the intermediate boson. Little can be said on general theoretical grounds about
the masses of new flavors, but interesting constraints arise from consistency requirements and from phenomenological relationships. Imposing the requirement that partialwave unitarity be respected at tree level in the reactions
(5.4)
t MU MD t & 550 GeV/c— (5 5)
where I"' denotes a heavy fermion, leads to restrictions on the heavy-fermion masses MF, which set the scale
(G~Mgv 2)'~ of the HFF couplings (Veltman 1977b; Chanowitz, Furman, and Hinchliffe, 1979). For a new doublet (D) of heavy quarks, this amounts to
(5.11a) (5.11b)
D q+ + 8'
for the quarks, and
I. ~X +8'
(5.12)
(5.13)
p +—p~ $~(QQ)+anything t = l+I (5.14)
because the weak decay rate for the constituents Q, Q
(ac M&) greatly exceeds the leptonic decay rate of heavy quarkonium ( ac M~). Therefore, we must rely on inclusive QQ production.
for the heavy lepton. In a theory with an expanded Higgs
sector, decays such as U~D+H+ may compete favor
ably with 8"emission. We shall not consider these potentially interesting charged Higgs modes any further. We now turn to estimates of the production cross sec
tions in p —p collisions. In contrast to the c arid b quarks,
which were signalled by the dilepton decays of the
P/J(cc) and Y(bb ) states, the existence of a heavy quark Q will not be signalled by the chain
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics
In lowest contributing order in the strong interactions, the elementary reactions leading to the Qg final state are
(5.15)
I
qq~gg, (5.16)
for which the Feynman graphs appear in Figs. 74 and 71. The gluon fusion cross section is (Combridge, 1979)
2
do — ~~s 6
dt" (gg gg) = ~ (t —Mg )(u —Mg )+
8w2
Mg (s —4Mg )
3(t —Mg )(u —Mg )
4 (t —Mg)(u —Mg) —2Mg(t/Mg)
(t —Mg )2
3(t —Mg )(u —Mg ) +Mg (u —t )
+ s (t Mg)— + [t~u]
(5.17)
In numerical calculations, we evaluate the strong coupling
constant a, at Q =4Mg. The cross section for Qg pro
duction in qq annihilations is
I
approximately one unit of rapidity. The satne is true for the products of intermediate boson decay,
-(qq QQ)
qq
8' ——+ ' Iv. (5.21)
4m.ag (t Mg)—+(u Mg)—+2Mgs
9~2 A.2
(5.18)
If the proton acquires its Qg content perturbatively, in
the manner described in Sec. II.B, the reaction
gQ gQ (5.19)
will occur with a negligible cross section. We shall therefore not include diffractive production of heavy flavors. We are open to the possibility that diffraction is an important mechanism, although it may lie outside the realm
of perturbative @CD. For a recent discussion of the pro
duction of a fourth quark generation in the context of a specific model for the diffractive component, see Barger
et al. (1984). The integrated cross sections for the reactions p~p~QQ+anything, evaluated using the parton distri
butions of Set 2, are shown as functions of the heavy quark mass Mg in Fig. 163. The parton distributions of
Set 1 lead to cross sections which are smaller by 10—20%
over the range of interest. Proton-antiproton collisions enjoy a competitive advantage only for
10 C
lIl
10
—1
10
10-8
10-3
Consequently, all the ultimate products of heavy quarks produced with ~y ~ & 1.5 should be contained in a detec
tor with angular coverage down to 2 .
To assess the capabilities of various colliders, we define an observable cross section to be one that yields at least
fifty detected Qg pairs in a run of 10 sec. (This could
well be an unnecessarily stringent criterion; it may suffice in practice to impose a topology cut and to reconstruct one heavy quark per event. ) The maximum quark mass that can be reached in a collider of given energy and luminosity depends sensitively upon the efficiency e for identi
2Mg/Vs )0.1; (5.20)
exploitation of this advantage requires high luminosities.
To better determine the detectability of the heavy quark pairs, we plot in Fig. 164 the cross section for production
of heavy quarks in the rapidity interval ~ y ~ & 1.5. Since
Qg production is dominated by gluon fusion, the pp and
pp cross sections are approximately equal except at very
large values of s, where there are very few events. The signature for heavy quark pairs will be events con
taining two 8'bosons and two quark jets. This should be
relatively free of conventional backgrounds. Typically the
mobility of products in the decays (5.11) and (5.12) will be
10-4
10-5
—B
10 0. 4 1.2 2 2. 8 quark M~~g
FICx. 163.. Integrated cross sections for pair heavy quarks in proton-proton (solid lines) antiproton (dashed lines) collisions, according to
tributions of Set 2, at Vs =2, 10, 20, 40, 70, and
3, 6 4. 4 (TeV/e*)
production of and protonthe parton dis100 TeV.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et aI.: Supercollider physics
2
10 in either pp or pp collisions. Again there is little differ
ence between pp and pp collisions in the regime of poten
tial experimental interest.
If the mass difference between members of a heavy quark doublet is large,
10
MU —Mg) )Mg,
then the decay chain
U~D+8 +
+q ~+8'
(5.23)
(5.24)
10
10
10-5
10 0, 4 1.2 2 2. 8 3.6 4. 4
quark Mass (TsV/c )
FIG. 164. Integrated cross sections for pair production of heavy quarks satisfying ~ yu ~, ) y& ~ & 1.5 in proton-proton
(solid lines) and proton-antiproton (dashed lines) collisions, according to the parton distributions of Set 2.
will lead to a signature of W+& W+W +2 jets for the
production of UU pairs. This sort of possibility emphasizes the benefits to be derived from the ability to identify intermediate bosons with high efficiency.
If the U-D mass difference is indeed large, a favorable production mechanism for the heavier partner may be
p
+—p ~ S'+~~~+ anything
L UD, (5.25)
which leads to a final state containing three intermediate bosons and two jets. Monte Carlo studies of specific examples should be quite revealing.
B. Pair production of heavy leptons
fying and measuring the products. Note, for example,
that if the intermediate boson can be identified only in its electronic and muonic decays, the efficiency cannot
exceed —15% per heavy quark, or 2% per QQ pair.
Bearing these numbers in mind, we plot in Fig. 165 the
maximum quark masses accessible for specified values of the effectiue integrated luminosity
W,ff=s I dt W (5.22)
I
Ldt (cm )
Mg{TeV/c )
We next consider the pair production of charged
sequential leptons (L+L ). We assume that
ML —Mg )Mg, (5.26)
and that the neutral lepton N is effectively stable and noninteracting. This includes the most conventional case in which N is essentially massless. The pair production of charged heavy leptons proceeds by the Drell- Yan (1970,1971) mechanism reviewed in Sec. IV.A. As noted there, the differential and total cross sect'iona are given by Eqs. (4.3), (4.11), and (4.12) times
the kinematic suppression factor (1—4MI. /M )'~
&((1+2ML /M ), where M is the invariant mass of the pair. We show in-Fig. 166 the cross section
do' f
dp 0
drJ
dM dy (5.27)
for the production of heavy-lepton pairs in the reaction
pp ~L +I. +anything (5.28)
20 40 60 80 IOO
~s {TeV)
FIG. 165. Maximum quark mass M~ accessible in pp (solid
lines) and pp (dashed lines) collisions for specified values of the
effectiue luminosity. Both quark and antiquark are restricted to ~ y ~ & 1.5. The actual collider luminosity required will be larger
by a factor of 1/(efficiency for identification and measurement
of the final state).
as a function of the lepton mass ML, . The same quantity is shown for pp collisions in Fig. 167. At large lepton
masses, pp enjoys a considerable advantage over pp in the
production rate. Whether this can be exploited depends upon backgrounds in the two cases and the number of events required to establish a signal.
One may search for a heavy-lepton (L+L ) signal in
two ways: by observing an excess in the 8'+ 8' produc
tion rate, or by selecting events in which %+8' appear
on opposite sides of the beam, with transverse momenta that do not balance. For the first case, the conventional
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics
Db
10
—3
10
gg w anything
modest lepton masses [O(100 GeV/c )] are likely to be
accessible. A realistic simulation will be required to make any precise statement. The unbalanced transverse momentum signature relies on the fact that in the sequence
p +—p ~I.+L, +anything
l—= 8 —+N'
(5.29)
10
10
10 0.2 0.4 0. 6 1 1.2 Ma ss (Te&/c~)
FICx. 166. Cross section do. /dy I» o for the production of
(L+L ) heavy-lepton pairs in pp collisions. The contributions
of both y and Z intermediate states are included, and the cal
culation is carried out using the parton distributions of Set 2.
pp ~ g'L + anything
8'+8' pair production treated in Sec. IV.C.2 presents a severe background. Comparison of the rates for the con
ventional electroweak process shown in Figs. 120—124
with the rates implied by Figs. 166 and 167 shows that if this signal can be used, a large number of events will be required to establish an effect. This means that only
10-8
the heavy leptons may emit the decay products out of the
production plane. If both 8'+ and 8' are emitted up,
for example, the event will have a large imbalance in visible pz, because the neutral leptons N will go undetected.
This topology should be both characteristic and free of
conventional background. Evidently the S'+— must be
detected in nonleptoni. .Channel. To assess the utility of
this signature requires a Monte Carlo simulation. The following rough exercise will serve to show why a detailed simulation might be interesting and worthwhile. We assume, as in the discussion of heavy quarks in Sec.
V.B, that the ultimate decay products of heavy leptons
produced in the rapidity interval —1.5 &y & 1.5 will be
captured in a standard "4vr" collider detector. Some frac
tion of these will survive the topological cut imposed by
the requirement of significant transverse momentum im
balance. A reasonable guess for this fraction is —',. The maximum lepton mass for which 25 such events will be detected is shown for various values of effective luminosity in Fig. 168. For effective luminosities in the range of
10 —10 cm, which correspond to thinkable combina
tions of detection efficiency and collider luminosity, a
40-TeV collider would be sensitive to heavy leptons with
masses up to 250 GeV/c . This possibility deserves more serious study. Another mechanism for the production of heavy lep
l.0
'Q
b
4
10
~ 0.8
C)
ca 0
CA CE3
eft IO
10
00
It 1 I
20 40 60 80 l00
II
0. 8 1 1, 2
«» (TeV/c')
FIG. 167. Cross section do/dy l„o for the production of
(L+L ) heavy-lepton pairs in pp collisions. Calculational de
tails are as for Fig. 166.
J~ (TeV)
FIG. 168. Maximum-charged lepton mass ML, accessible in
L+L production in pp (solid fines) and pp (dashed lines) col
lisions for specified values of the effective luminosity. The actual collider luminosity required will be larger by a factor of 1/(ef
ficiency for identification and measurement of the final state).
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et af.: Supercollider physics 647
d &tJ.
dt
~a'~ U,, ~' (u —Mg)(u —M„')
12xws (s —Mw) +Mwt w
tons is the reaction
p +—p~l. —+N +anything,
which proceeds by the elementary process + +0
a.eg ~ ~.i~~i ~L
The differential cross section is
(5.30)
(5.31)
(5.32)
10-2
—3
10
C
nD
'0
b0 4
10
Ps
(s —Mw) +MwI w
2 22
MI —M~
2
X 1+ 3 (5.33)
where Uz is an element of the Kobayashi and Maskawa
(1973) quark mixing matrix, and the total cross section is
m.a fU,~/
O~J. = 2
48xp 10-5
with
ML +M~
1 —2 +
S
2 I /2
ML —M~
We show in Fig. 169 the cross section
(5.34)
10 o. e 1.4 1.8 Moss (TeV/c*)
170. Cross section dcrldy ~» o for the production of
(L N ) pairs in pp collisions. Calculational details are as in
Fig. 169.
= J dVs (5.35)
0 dV$ dy y=o
for the production of (L +N ) pairs i—n pp collisions as a
function of the heavy-lepton mass Mz. The same quanti
ty is shown for pp collisions in Fig. 170. In these exam
ples, we have assumed the mass of the neutral partner N
10-2
to be negligible. The yields are considerably larger, for a
given value of MI, than those for L+L pairs, because
of the accessibility of lower L+—N pair masses. For large
values of ML, pp collisions display the familiar advantage
of valence quark —valence antiquark collisions.
To estimate the discovery reach of high-energy colliders, we determine the effective luminosity required to es
tablish a 5cr excess of
10-3
C
'0
'Db 4
10
(5.36)
final states, in which the neutral leptons escape undetect
ed. For this purpose, we compare the yield of L +No
events in the rapidity interval —1.5&y &1.5 with the
background from the process
p p —+8'Z
10-5
I I I I I I I I .I I
0.8 0.6 1 1.4 i.e
Moss (TeV/c )
FIC». 169. Cross section dc» jdy ~» 0 for the production of
(L +—N ) pairs in pp collisions. The N is assumed to be mass
les's, and the parton distributions are those of Set 2.
(5.37)
where the gauge bosons both lie in the rapidity interval
—2.5&y &2.5. The larger bin for the background is
chosen to match the mobility of 8' +—from I.+—decay.
We show in Fig. 171 the maximum lepton mass for
which a 5o. excess can be established for various values of
effective luminosity. As usual, these effective luminosities
must be divided by the efficiency Ew for W detection to
obtain the collider luminosity. For effective luminosities
in the range 10 —10 cm, the reach in ML is typically
two times as large in the I.+—X channel as in the I.+I.
channel.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


648 Eichten et al. : Supercollider physics
09
O
I- 0. 8
0) 0
0. 6
0. 4
M~/M~, and with the scaling variable r=M~ /s. We
show in Figs. 172 and 173 the cross sections for W'-+ and
8' produced in pp and pp collisions in the rapidity in
terval —1.5&y~ &1.5. At the largest masses, this re
striction does not appreciably reduce the yield. As we have seen in other similar circumstances, the advantage of
pp collisions over pp collisions becomes significant for
v~&0. 1.
There are two possibilities for detection: the leptonic decay modes
8" eve
(5.39)
0. 1
I
20
I
40
I
60 80
~s (7ev)
l
100
which occur with branching ratios
I ( W'~iv)/I ( W'~all) = 1/4ng, (5.40)
where ng is the number of fermion generations, or the
nonleptonic decays
FICx. 171. Maximum-charged lepton mass Ml accessible in
L +—N production in pp (solid lines} and pp (dashed lines) for
specified values of the effective luminosity. The actual collider luminosity required will be larger by a factor of 1/(efficiency for the identification and measurement of the final state).
8"~jet+jet,
for which the branching ratio is
I ( W'~jet+jet)/I ( W'~all) = ~ .
(5.41)
(5.42)
C. New electroweak gauge bosons
A number of proposals have been advanced for enlarging the electroweak gauge group beyond the
SU(2)L, U(1) r of the standard model. One class contains
the "left-right symmetric" models (Pati and Salam, 1974; Mohapatra and Pati, 1975; Mohapatra and Senjanovic, 1981; Mohapatra, 1983) based on the gauge group
In the case of the W+— and Z of the Weinberg-Salam model, the QCD two-jet background is about an order of magnitude larger than the expected signal. Whether this circumstance continues for intermediate bosons in the TeV/c regime depends, inter alia, upon the two-jet mass resolution that can be achieved. This is another question that is well suited for detailed simulations. We adopt as a discovery criterion the requirement that
SU(2)L SU(2)gU(1)r, (5.38) 10
J3 E
c
which restores parity invariance at high energies. Other models, notably the electroweak sector derived from the SO(10) unified theory, exhibit additional U( 1) invariances. These will contain extra neutral gauge bosons. A general discussion was given by Georgi and Weinberg (1978).
Prospects for detecting a second Z have been analyzed
recently by I.eung and Rosner (1983).
All of these models have new gauge coupling constants
which are of the order of the SU(2)L coupling constant of the standard model. They imply the existence of new gauge bosons with masses of a few hundred GeV/c or more. In most interesting models, these new gauge bosons decay to the ordinary quarks and leptons (perhaps augmented by right-handed neutrinos). Roughly speak
ing, the decay rates of a 8" will correspond to those of the familiar W, times M~/Mn. The heavier gauge bosons will therefore also be relatively narrow and prominent objects. To obtain a reasonable estimate of the cross
sections for the production of additional W or Z bosons, we assume that the new bosons have the same gauge cou
plings to light leptons and quarks as do the familiar 8'
and Z
The differential and total cross sections for W' +—production are then given by (4.35) and (4.37) times
1
c
c0 10
H
10
10
10-4
10 9 10
Mass (TeV/c*)
FICx. 172. Integrated cross sections for the production of 8 '+
(solid lines) or W' (dashed lines) with rapidities ~ys ~ &1.5 in
proton-proton collisions, according to the parton distributions of
Set 2, at ~s = 2, 10, 20, 40, 70 and 100 TeV.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 649
2O
2 Qch
C 10
10-2
10-4
lyl C
makes itself apparent for integrated luminosities in excess
of about 10 cm . For example, a 40-TeV pp collider
can reach masses of 2.3, 4. 1, and 6.5 TeV/c for integrat
ed luminosities of 10, 10, and 10 cm . A pp
machine of the same energy can attain 2.4, 4.7, and S.O
TeV/c . The situation is rather similar for the production and detection of neutral gauge bosons. In this case we estirnate the differential and integrated cross sections from Eqs. (4.39) and (4.41) times Mz/Mz, with the scaling
variable ~=Mz /s. The resulting cross sections for Z ' production in the rapidity interval ~ yz ~ & 1.5 in pp and
pp collisions are shown in Figs. 175 and 176. Again, the
advantage of pp collisions is significant only for V v & 0.1.
For a neutral gauge boson with couplings identical to
those of the standard model Z, the leptonic decays
e+e
zoi (5.43)
PP
10-5 I I
4
.5
II I I
6 V 8 9 10
Mass (TeV/c*)
each occur with branching fraction
I (Zo'~l+1 )/I'(Z ' —+all)=9%/ns, (5.44)
FIG. 173. Integrated cross sections for the production of W'+
or W' with rapidities ~ys ~ &1.5 in proton-antiproton col
lisions, according to the parton distributions of Set 2.
1000 gauge bosons be produced in the rapidity interval ~ y~ ~ & 1.5. Unless the branching ratio for leptonic de
cay is much smaller than for the ordinary W +—, this should allow the establishment of a convincing signal in either the electron channel or the muon channel. The resulting discovery limits are shown in Fig. 174. The larger production rate for heavy gauge bosons in pp collisions
1s
I (Z '~jet+jet)/I (Z '~all) = —' , . (5.46)
As for the W'+-, we regard 1000 neutral gauge bosons
produced in ~yz. ~ &1.5 as the minimum number required for discovery. The discovery limits implied by this requirement are displayed in Fig. 177. Once again, the
wher ens 'is the number of fermion generations The.
branching ratio for the nonleptonic decays
Z '~jet+jet (5.45)
10
I
@ddt(cm ') r / @o
}0
t
~CCM1
O 10-2
+
C ).5
10-2
10-3
10
I
20 80
I II
40 60 l00
Xs {TeV) FIG. 174. Maximum mass of a new charged intermediate boson for which 10 events are produced with ~ys ~ &1.5 at the
stated integrated luminosities in proton-proton collisions (solid lines) and in proton-antiproton collisions (dashed lines).
20-4
10-5 I
1 2 3 4, 5 6 V 8 9' 10
Mass (TcV/c )
FICx. -175. Integrated cross sections for the production of Z
with rapidity ~yz ~ &1.5 in proton-proton collisions, according
to the parton distributions of Set 2.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


650 Eichten et al. : Supercollider physics
iO I
C
l), C
Co i0
h4
lyl C 1.5
iO -3
10
10-5 I I I I I
23456
III
7 8 9 10
Mass (Tev/c~)
FIG. 176. Integrated cross sections for the production of Z
with rapidity ~yz ~ &1.5 in proton-antiproton collisions, according to the parton distributions of Set 2.
12
advantage of pp collisions in qq luminosity becomes ap
parent for integrated luminosities greater than 10 cm At 40 TeV, a pp collider can reach 1.7, 3.3, and 5.5
TeV/c for integrated luminosities of 10, 10, and 10
cm, whereas a pp collider can reach 1.9, 3.8, and 7.1
TeV/c . We may expect the same relative performance
whatever the precise structure of the Z ' couplings to light fermions, so long as they are of universal (gauge) strength.
l3. Summary
8 +8' +missing pz (5.47)
and of new gauge bosons in the two-jet channel are re
quired. For the leptonic decays of very massive W' +—, the
consequences of the expected charge asymmetry [see, e.g.,
Rosner et al. (1984)] are worth pursuing.
Yl. TECHNICOLOR
We have already given an assessment of the capabilities
of multi-TeV colliders for the discovery of new quarks, leptons, and gauge bosons in Figs. 165, 168, 171, 174, and 177. Roughly speaking, the discovery limits lie in the
range 1—2 TeV/c for quarks, 0.1—0.7 TeV/c for
sequential charged leptons, and 4—5 TeV/c for new gauge bosons, for colliders with c.m. energies and lumino
sities of the magnitudes being contemplated. Within the range of collider parameters under consideration, the reach of a 40-TeV collider is about twice that of a 10-TeV collider at the same luminosity. Increasing the collider energy to 100 TeV extends its reach by a factor of about
1.5 over that of the 40-TeV machine. These gains are somewhat smaller at low 1uminosities, and somewhat larger at high luminosities. For the minimal extensions we have discussed, a pp machine holds little advantage in
production rates over a pp machine of the same energy
and luminosity. More complicated comparisons, such as the physics tradeoff between a pp machine of given ener
gy and luminosity versus a pp machine of higher energy but lower luminosity can be drawn from the summary figures 165, 168, 171, 174, and 177. Not for the last time, we note that there are significant benefits attached to detecting intermediate bosons in their nonleptonic modes. Detailed studies of the observability of heavy leptons in the final state
10
jgdt (cm z)~.o
10
I
20 40 60 ~s (TeV)
80 100
FIG. 177. Maximum mass of a new neutral intermediate boson
for which 10' events are produced with ~ yz ~ & 1.5 at the stated integrated luminosities in proton-proton collisions (solid lines) and in proton-antiproton collisions {dashed lines).
A. Motivation
In the standard electroweak model, the SU(2)L, U(1)y local gauge symmetry is spontaneously broken to U(1),~
through the medium of auxiliary, elementary scalar fields known as Higgs bosons. The self-interactions of the Higgs scalars select a vacuum, or minimum energy state, which does not manifest the full gauge symmetry of the
I.agrangian. In so doing, they endow the gauge bosons
and the elementary fermions of the theory with masses. Indeed, three of the four auxiliary scalars introduced in the minimal model become the longitudinal components
of W+, 8', and Zo. The fourth emerges as the physi
cal Higgs boson, which has been the object of our atten
tion in Sec. IV.D. In spite of, or indeed because of, the phenomenological successes of the standard model, the elementary scalar solution to spontaneous symmetry breaking m.ay be criticized as arbitrary, ambiguous, or even (Wilson, 1971) theoretically inconsistent. The principal objections concern the multitude of arbitrary parameters associated with
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eiehten et af.: Supercollider physics 651
g2 0 0 g2
—0 0 00
00 00
gggf
gà g
(6.1)
A convenient summary and reprint collection appears in Farhi and Jackiw (1982).
the Higgs potential and the Yukawa couplings that generate fermion masses, and the instability of the masses of elementary scalars in interacting field theory. One hopes for a better, more restrictive solution, with greater predictive power. A promising approach is suggested by another manifes
tation of spontaneous symmetry breaking in nature, the superconducting phase transition. The macroscopic Cxinzburg-Landau (1950) order parameter which acquires a nonzero vacuum expectation value in the superconducting state corresponds to the wave function of superconducting charges. In the microscopic Bardeen-CooperSchrieffer (1962) theory, the dynamical origin of the order parameter is identified with the formation of bound states of elementary fermions, the Cooper pairs of electrons. The hope of the general approach known as dynamical symmetry breaking is that the dynamics of the fundamental gauge interactions will generate scalar bound states, and that these will assume the role heretofore assigned to the Higgs fields. Could this occur for the electroweak theory without the introduction of any new interactions or fundamental constituents? It is quite, instructive to see how QCD may act
to hide the SU(2)L, SU(1)z gauge symmetry. Consider the conventional SU(3)„&„I3ISU(2)z U(l ) z gauge theory ap
plied to massless up and down quarks, and assume that the electroweak sector may be treated as a -perturbation. The QCD Lagrangian has an exact chiral SU(2)1 SU(2)z symmetry. It is generally supposed that the strong color forces spontaneously break the chiral symmetry SU(2)L,
SU(2)z ~SU(2). As usual, the spontaneous breaking of a global continuous symmetry is accompanied by the ap
pearance of massless Goldstone bosons, one for ea,ch broken generator of the global symmetry. In the case at hand, these are the three pions. (We attribute their nonzero masses in the. real world to small quark masses in the Lagrangian. ) The electroweak gauge bosons couple to
broken generators of the chiral SU(2)L SU(2)z symmetry group. These broken generators correspond to axial currents whose coupling to the pions is measured by the
pion decay constant f„. Consequently the electroweak
gauge bosons acquire masses of order gf, where g is the
coupling constant of the SU(2)L, gauge symmetry. The massless pions disappear from the physical spectrum,
having become the longitudinal components of W+, W
andZ . This is summarized by a mass matrix (Weinstein, 1973; Weinberg, 1979a; Susskind, 1979)
in which rows and columns are labeled by the SU(2)L, and
U(1)r gauge bosons ( W+, W, W, B), and g'/2 is the
coupling constant for the weak-hypercharge group U(1) ~.
The mass matrix of the conventional Weinberg-Salam
theory has precisely the form of (6.1), with f =93 MeV
replaced by the vacuum expectation value
v = ( GFV 2) '~ = 247 GeV . (6.2).
The spectrum of physical gauge bosons therefore includes the massless photon and the neutral intermediate boson
Z, with
Mz =(g'+g') f' /4,
as well as the charged intermediate bosons 8'+—, with
Mw=g'f /4
The conventional mass ratio
Mz/Mg ——(g +g' )/g =1/cos 8p
is preserved, but the masses themselves,
Mp =30 MeV/c
Mz =34 MeV/c
are scaled down by a factor
f /v=1/2650 .
(6.3)
(6.4)
(6.5)
(6.6)
(6.7)
The chiral symmetry breaking of QCD thus cannot be the source of electroweak symmetry breaking. Let us also note that one of the tasks of the Higgs scalars, the generation of fermion (including lepton) masses, is not addressed at all by this mechanism. Although this simplest .implementation of dynamical symmetry breaking docs not succeed, it points the way to more realistic models. One natural response to the quantitative failure of the scheme described above is to postulate a new set of elementary fermions with interactions governed by a new strong-interaction gauge group. The
term technicolor has come to stand both for this style of dynamical symmetry breaking and for the specific gauge group underlying the new dynamics. In the next section (VI.B) we introduce the minimal technicolor model of Weinberg (1976,1979) and Susskind (1979). This model shows how the generation of intermediate boson masses could arise without fundamental scalars or unnatural adjustments of parameters. However, it offers no explanation for the origin of quark and lepton masses. We introduce in Sec. VI.C a nonminimal "extended technicolor" model due to Farhi and Susskind (1979) which shows how fermion masses might realistically be generated. Although this model is not rich enough to describe the real world, it has many observable consequences which would have to be present in any complete
model of 'this type.
Sections VI.D and VI.E are devoted to some of the prominent experimental signatures for technicolor. There we discuss specifically the production and detection of single technihadrons (VI.D) and of technihadron pairs
Rev. Mod. Phys. , Vol. 56, No. 4, October 1 984


652 Eichten et al. : Supercollider physics
(VI.E). A summary of collider capabilities is given in Sec.
VI.F. Additional background material on technicolor, its phenomenology, and comparison with models involving elementary scalars may be found in the reviews by Farhi and Susskind (1981),Lane (1982), and Kaul (1983).
B. The minimal technicolor model
The minimal model of Weinberg (1976b, 1979a) and Susskind (1979) is built of a chiral doublet of massless technifermions U and D which are taken for simplicity to be color singlets. Under the technicolor gauge group GTC, the technifermions transform according to a com
plex representation. It is convenient for illustrative pur
poses to choose GTC ——SU(N)TC, and to assign the technifermions to the fundamental N representation. With these assignments the technicolor, or TC, Lagrangian exhibits an exact chiral SU(2)L @SU(2}a symmetry. At an energy scale of order ATC=O(1 TeV), the technicolor interactions become strong and the chiral symmetry is spontaneously broken down to (vector) SU(2), the isospin group of the technifermions. As a consequence of the spontaneous symmetry breaking, three Goldstone bosons appear. These are the mass
less technipions, J =0 + isovector states designated
+0
HATT p fT Tp &T ~
The couplings of the technifermions to the electroweak gauge bosons are specified by the conventional SU(2)L, U(1)y assignments, namely, a single left-handed weak-isospin doublet
U (6.8)
F =(Gpv 2) (6.14)
then after the electroweak interaction is turned on, the
W+—and Z will acquire the canonical masses
Mw ——g /4G+W2=ma/csin ew
Mz~=Mw/cos Ow .
(6.15)
(6.16)
The massless technipions disappear from the physical spectrum, having assumed the role of the longitudinal
components of the intermediate bosons. Knowing the spectrum of ordinary hadrons, and attributing its character to @CD, we may infer the remaining
spectrum of technihadrons. It will include
an isotopic triplet of J =1 technirhos, pz, pr, pT,
with M (p z ) = O(1 TeV/c ),
an isoscalar J = 1 techniomega, AT, with
M(d'or )=O(1 TeV/c ), an isoscalar pseudoscalar technieta, g z., with
M(gz)=O(1 TeV/c ),
an isoscalar J =0++ technisigma, o.T, with
M(oz')=O(1 TeV/c ),
plus other massive scalars, axial vectors, and tensors. The oz is the analog of the physical Higgs scalar in the Weinberg-Salam model. In addition to these ( TT) tech
nimesons, there will be a rich spectrum of (T ) techni
baryons. Some of these might well be stable against decay, within technicolor.
In the absence of coupling to the electroweak sector, this techniworld mimics the QCD spectrum with two quark flavors. Large N arguments for the mass and width of the technirho (Dimopoulos, 1980; Dimopoulos, Raby, and Kane, 1981)give the estimates
with weak hypercharge
Y(QI. }=o
and two right-handed weak-isospin singlets
(6.9)
(6.10)
' 1/2
M(pz ) =M(p)
and
=(2 TeV/c 2 ) 3
' 1/2
(6.17)
with weak hypercharge
Y(Ug ) =1,
3
I (pz ~mznz. )=T'(p~~n) 1V
.M(pz ) M(p)
Y(Da)= —1 .
(6.11) X[1—4M(m. ) /M(p) )
With these assignments, the technifermion charges are
given by the Gell-Mann-Nishijima formula =(0.5 TeV) 3
1V
3/2
(6.18)
as
Q =I3+—' ,Y
Q(U)= —',,
(6.12) where the technipion mass has been neglected compared
to M(pz }. For the popular choice N=4, we find
M(p, )=1.77 Tev/c',
Q(D)= ——',, (6.13)
I (pz' m z m T )=325 GeV . (6.19)
and the electroweak sector is free of anomalies.
If the technicolor scale ATC is chosen so that the technipion decay constant is
The techniomega is expected to have approximately the same mass as the technirho, and to decay principally into three technipions.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984,


Eichten et af.: Supercollider physics. 653
We have already remarked that this minimal technicolor model does not account for the masses of the ordinary fermions. This shortcoming may be remedied by the extended technicolor strategy (Dimopoulos and Susskind, 1979; Eichten and Lane, 1980) to be explained below. Since the additional complication of extended technicolor is of little observational import in the framework of the minimal model, we shall not discuss it further in this context. In hadron-hadron collisions, the technifermions of the minimal model will be pair produced by electroweak processes. One possible experimental signature is the creation of stable technibaryons, which for all odd values of N would carry half-integer charges. We are not confident in estimating the production rate for these states, except to note that it cannot exceed the overall rate of technifermion pair production, which will be minuscule on the order of the Drell-Yan cross section. The signature is nevertheless an important one to bear in mind. Less dependent on details, and thus more characteristic
I
of the minimal technicolor scheme, are the expected modifications to electroweak processes in the 1-TeV regime. The most prominent of these are the contributions of the s-channel technirho to the pair production of gauge
bosons. Because of the strong coupling of technirhos to
pairs of longitudinal W's or Z's (the erstwhile technipions), the processes (Susskind, 1979)
q;q;~(y or Z )~pT~Wo+8'o (6.20)
+ + +p
q;qj ~ S'—~pT——+8'p Zp, (6.21)
where the subscript 0 denotes longitudinal polarization, will lead to significant enhancements in the pairproduction cross sections. Including the s-channel technirho enhancement, the
differential cross sections for production of W+ W and W
+—Z are given by (4.48) for W'+8', with the coeffi
cient of (u t Mw)/s re—placed by
6M@
+ s —Mz
I; +
v3;(I —xw)
s
sA.—Mz
2 12M~
4 —1+ s
I. +R
4(1 —xw)2
s L, S
s Mz t3 (1—xw. ) s —Mz
+ L,; +Rg
4(1 —xw)
Mp
(s —M )+M I
~T' ~T' I r
(6.22)
and by (4.60) for 8'Z, with
Mp
(9—8xw)~ 2 2 2 +8(1—xw),
(s —M,', )'+M,', r,', (6.23) at 3/s =20 TeV,
—6
10
1.1& 10 nb
2. 1& 10 nb (6.25)
1.5 TeV/c &~ & 2. 1 TeV/c (6.24)
amount to
where the notation is that of Sec. IV.
We show in Fig. 178 the mass spectrum of W+W pairs produced in pp collisions at 20, 40, and 100 TeV,
with and without the technirho enhancement. Both intermediate bosons are required to satisfy ~y ~ &1.5. For
this example, we have adopted the technirho parameters given in (6.19), and used the parton distributions of Set 2. The rates are substantially unchanged if the parton distributions of Set 1 are substituted. The yields are slightly higher in the neighborhood of the pz enhancement in pp
collisions. This is a 25% effect at 40 TeV and a 10% effect at 100 TeV. The technirho enhancement ainounts to nearly a dou
bling of the cross section in the resonance region. However, because the absolute rates are small, the convincing ob
servation of this enhancement makes nontrivial demands on both collider and experiment. Let us now see this quantitatively.
The cross sections for 8'+8' pair production integrated over the resonance region
O
4P
C7
10
D0
+ anything
—8
10
1.5
g
10 1.2
I
1.4
I
1.6
I. I
2 2. 2 2. 4
Pair Maes (Tev/c )
FIG. 178. Mass spectrum of 8'+ 8' pairs produced in pp col
lisions, according to the parton distributions of Set 2. Both 8'+
and W must satisfy ~ y ~ &1.5. The cross sections are shown with (solid lines) and without (dashed lines) the technirho enhancement of Eq. (6.22). The technirho parameters are those
of Eq. (6.19).
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


654 Eichten et a/. : SupercoIlider physics
do. 3.0X 10 nb
5.4X10-' nb
at Vs =40 TeV, and
r
f
do. 8.0X 10 nb 14X 10 nb
(6.26)
(6.27)
O
C
10 7
'v0
—6
10 I I I I
:
pp = ZW ~ZW ~ anything
r
0.52, Ms =20 TeV ew & 0.36, v s =40 TeV 0.24, Vs =100 TeV .
(6.28)
at Vs =100 TeV. In each case the larger number includes the technirho contribution. In this channel the enhancement is relatively modest, because the pT pole
multiplies a term in (6.22) that is numerically small. In a standard run with integrated luminosity of 10
cm, the number of excess events will be 100 on a back
ground of 110 at 20 TeV, 240 on a background of 300 at 40 TeV, and 600 on a background of 800 at 100 TeV. We require that the enhancement consist of a least 25 detected events, and that the signal represent a five standard deviation excess over the background. This criterion means
that each 8' must be detected with an efficiency of
10
—9
10 1.2
I
1.8
II
2 2. 2 2. 4 Pair M~pg (Tev/c~)
FIG. 179. Mass spectrum of 8 +Z and 8' Z pairs produced in pp collisions, according to the parton distributions of Set 2.
Both intermediate bosons must satisfy ~y ~ &1.5. The cross sections are shown both with (solid lines) and without (dashed lines) the technirho enhancement of Eq. (6.23). The technirho
parameters are those of Eq. (6.19).
This is clearly quite demanding, and in particular precludes reliance on Ieptonic decay modes except perhaps at the very highest energies. The requirements are relaxed somewhat if the rapidity cuts are softened to ~ y ~ &2.5,
and if a lower statistical significance is accepted. All these conclusions of course depend strongly upon the assumed pT parameters.
The situation is somewhat more encouraging for the pT
enhancement in the 8' +—Z channel. The mass spectrum
of 8'+Z plus 8' Z pairs produced in pp collisions at 10,
20, 40, and 100 TeV is shown with and without the pTcontribution in Fig. 179. The same remarks about structure functions and the pp vs pp comparison apply as be
fore. In the charged channels, the technirho enhancement results in a cross section that is about four times the standard-model rate in the resonance region. The cross
sections for W+Z plus 8' Z pair production integrated over the resonance region (6.24) are
3.2X10—' nb
14X 10 nb (6.32)
1, Vs =10 TeV 0.41, Vs =20 TeV
~~w~z ~ 0.24, vs =40 TeV 0. 15, v s =100 TeV .
(6.33)
at vs =100 TeV. In each case the larger number includes the pT enhancement.
In a standard run with integrated luminosity of 10
cm, the number of excess events will be 28 on a back
ground of 10 at 10 TeV, 150 on a background of 50 at 20
TeV, 420 on a background of 130 at 40 TeV, and 1080 on a background of 320 at 100 TeV. To establish the enhancement at the 5o level therefore requires efficiencies
e~ and ez for detection of W+ and Z of
do. , 1.0X 10 nb
d~ 3.8X10 6 nb
at Vs =10 TeV,
do 4 8X10 nb
2.0X10—'nb
at ~s =20 TeV,
do. 1.3X 10 nb
5.5X10—' nb
I
at Ms =40 TeV, and
(6.29)
(6.30)
(6.31)
These are less demanding than the requirements (6.28) for observation of the technirho enhancement in the neutral channel. If it should be necessary to rely on detection of the non
leptonic decay modes of the intermediate bosons, we must
face the possibility that the 8' +— and Z cannot be separated in the two-jet invariant mass distribution. In this case, the quantity of interest is the sum of the
8'+8', 8'+Z, 8' Z, and Z Z cross sections. The
last of these receives no technirho enhancement, but is a small background. The resulting required detection efficiencies are comparable to those obtained in the discussion of p—T, and the same general conclusions apply. In this case, one will not be able to establish that the tech
Rev. Mod. Phys. , Vol. 56, No. 4, October 4984


Eichten et al. : Supercollider physics 655
nirho occurs with charges + 1, 0, and —1.
As in our treatment of gauge boson pair production in the standard electroweak theory, a key remaining question is whether the four-jet QCD background will compromise
the detection of nonleptonic 8'and Z decays.
C. The Farhi-Susskind model
The minimal model just presented illustrates the general strategy and some of the consequences of a technicolor implementation of dynamical electroweak symmetry breaking. In a number of respects, it is not sufficiently rich to describe the world as we know it. In any of the more nearly realistic technicolor models produced so far, there are at least four flavors of technifermions. As a consequence, the chiral flavor group is larger than SU(2)LSU(2)~, so that more than three massless technipions result from the spontaneous breakdown of chiral symmetry. Just as before, three of these will be incorporated into the electroweak gauge bosons. The others remain as physical spinless particles. Of course, these cannot and do not remain massless. Colornonsinglet technimesons, if any, acquire most of their mass from QCD contributions (Dimopoulos, 1980; Peskin, 1980; Preskill, 1981; Dimopoulos, Raby, and Kane, 1981). The color-singlet technipions acquire mass from electroweak effects and from extended technicolor interactions (Eichten and Lane, 1980). Extended technicolor provides a mechanism for endowing the ordinary quarks and leptons with masses. This is accomplished by embedding the technicolor gauge group GTC into a larger extended technicolor gauge group GETc&GTc which couples quarks and leptons to the
techifermions. It is assumed that the breakdown
gETC —+GTC occurs at the energy scale
AETC-30 —300 TeV (6.34)
and that massive ETC gauge boson exchange generates quark and lepton bare masses of order
+TC ~+ETC
3 2 (6.35)
ETC gauge boson exchange also induces contact interac
tions of the kind discussed in Sec. VIII on compositeness. Unfortunately, no one has succeeded in constructing an extended technicolor model which is at all realistic. Whichever of these mechanisms is responsible for the generation of technipion masses, the expected masses all are considerably less than the characteristic 1-TeV scale of technicolor. Equally important, the couplings of tech
nipions to SU(3), SU(2)L SU(1)r gauge bosons is known
fairly reliably within any given model, and almost all of them will be copiously produced in a multi-TeV hadron collider. The challenge, as we shall see, lies in detecting these particles in the collider environment. In this section we introduce a simple toy technicolor model due to Farhi and Susskind (1979), which has quite
a rich spectrum of technipions and technivector mesons. The version of the model we consider has been developed
Gf ——SU(8)L @SU(8)~I33U(1)v . (6.37)
This symmetry is spontaneously broken down to SU(8)~U(1)~. The breakdown is accompanied by the
appearance of 8 —1 massless technipions which belong to the adjoint, or 63-dimensional representation of the residual SU(8)z flavor symmetry group. So far as the technicolor interactions are concerned, these are all pseudo
scalars. The technimesons are enumerated in Table II.
There are seven color singlets, of which three (nT+, n z, m z ).
become the longitudinal components of the electroweak
gauge bosons. The remaining four are denoted P+, P,
P, and P '. At least these color-singlet technipions
in detail by Dimopoulos (1980), Peskin (1980), Preskill (1981), and Dimopoulos, Raby, and Kane (1981). This model cannot be correct in detail, but many of the observable consequences are typical of all quasirealistic technicolor models. We now discuss in turn the technifermion content, the spectrum and properties of the technipions and technirhos, the interactions of technimesons
with SU(3), I3 SU(2)z e U(1)z gauge bosons (i.e., the
means of producing technimesons), and the interactions of technimesons with quarks and leptons (which determine the means of detection). The elementary technifermions in this model are a pair
of color-triplet techniquarks Q=(U, D), and a pair of
color-singlet technileptons I =(N, E). Both left-handed
and right-handed components of the technifermions are assigned to the same complex representation of the technicolor group GTc. For specific numerical estimates, we
shall assume that GTc ——SU(N)Tc, with N=4, and that
the nf =2&&3+ 2=8 "flavors" of technifermions lie in
the fundamental 4 representation. Under SU(3),
SU(2)iU(1)~, the technifermions transform as follows:
Ug. (3, 1,Y+1)
QL, ——( U, D)g.(3,2, Y)Dg.(3, 1, Y—1)
(6.36)
Ng. (1,1, —3Y+ 1)
Ll. ——(N, E)L.(1,2, —3Y)Eg.(1,1, —3Y—1) .
The weak hypercharge assignments ensure the absence of
anomalies in all gauge currents. For the choice Y= —',, the techniquark and technilepton charges [compare (6.12)] are those of the ordinary quarks and leptons. To determine the chiral flavor symmetry group Gf of
the technimesons, we need only notice that all but the TC interactions themselves are feeble at the technicolor scale of about 1 TeV. In first approximation, QCD may be ignored by virtue of its asymptotic freedom, while the broken extended technicolor interactions are suppressed by at
least (ATc/AETc) . (We note in passing that the asymp
totic freedom of QCD is actually lost above the technifer
mion threshold —1 TeV in such a theory. We shall not explore here the consequences of this fact.) Because both left-handed and right-handed technifermions belong to the same complex representation of GTc, it follows that the techniflavor group is
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et ai.: Supercoilider physics
TABLE II. Technipions and technivector mesons in the model of Farhi and Susskind (1979). [See also Peskin (1980) and Preskill
(1981).] For unit normalization, the technifermion states should be divided by V N. The SU(8)~ matrices are 8X8 matrices written
in 4X4 block form. The A,, are the 15 orthonormal generators of SU(4). The SU(3), indices a, p run over 1,2,3 for color triplets; the
index a runs over 1, . . . , 8 for color octets. Repeated indices are to be summed. The symbol A, + denotes A,, +Q,, +1 for a=9, 11,
and 13. The weak hypercharge parameter Yis given in (6.36).
States Technifermion wave function Color Charge SU(8) ~ matrices
m+T, P2+
00
~TsP2
HATT, P2
p+ p+
pO 0
P,P1
pO' pO'
%)TED
COT
11
P3 p
1/2 i U D +NE)
(1/V 8) i U U DD—+NN EE)
1/2 i D U +EN)
(1/~12) ~ U D 3NE )
(1/V 24) i U U DD —3(NN —EE))
(1/V 12) i D U 3EN)
(1/V 24) i U U +D D 3(NN+E—E))
(1/V 8) i U U +D D +NN+EE)
(1,0)
(1,0)
(0,0)
(0,0)
0
0
0
0
2Y+1
0I
1/V 8
I0
'/4 0 -I
00
1/V 8
0 A15
1/2
0
o —~15
00
1./2
0
'/~8 o ~15
I0
1/4
0 A,, +
1/V 8
00
P3 p3 (1/V2 ~ U N DE)— (1,0)
A&a +
1/4
0
p —1 —1
3 sp3
n —1 ——1
P3 ~p3
0 —0
P3,p3
1 —1
P3,p
I D.N)
iND )
(1/V 2) i NU ED )— (1,0)
2Y —1
1 —2Y
—1 —2Y
00 o
a+
0 A,,
1/V 8
0
'/4 0
00 o
a
II
P3 p3 (1/V 2) i U.N+D. E) {0,0)
ka +
1/4
0
0
II
p3 p3
p+ p+
00
P8 IP8
(1/V2) ~ NU +ED )
(A,, /V 2) p i U Dp)
(A,,/2) pi U Up DDp)
(0,0)
(1,0) 0
1/4
0 1/2
1/V 8
0
0
Ps Ips
0' 0'
P8 QTsP8
(A,, /V 2) p i DpU )
(A,, /2) pi U Up+D Dp) (0,0) 0
00
'/2 A,. 0
A,a 0
1/V 8 a
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et Bl.: Supercollider physics 657
occur in all nonminimal technicolor models. The FarhiSusskind model contains in addition 24 color-triplet QL and QL bound states designated P3 (sometimes called leptoquarks), and 32 color-octet QQ bound states P8+, P8,
Ps, and Ps' (also known as
tlat.
). All of these are classi
fied in Table II according to their quantum numbers in the natural SU(4)SU(2) decomposition of SU(8). Here SU(4) is the Q-L symmetry group of which SU(3), is a subgroup. The SU(2) refers to the total weak-isospin group which reflects the family symmetries among U and
D on the one hand and N and E on the other. The pseudoscalar decay constant for these states is
F =(G~nf/W2) =124 GeV . (6.38)
The color-singlet technipions are the closest analogs in this model to the charged and neutral Higgs bosons in nonminimal electroweak models with elementary scalars.
The P+ and P acquire mass from both electroweak and
extended technicolor interactions, while the P and P ' masses arise from ETC alone. These masses have been estimated as (Eichten and Lane, 1980)
8 GeV/c &M(P +—) &40 GeV/c
The decay modes and branching ratios of the neutral technirhos are listed in Table III, where the partial decay rates are estimated as (Dimopoulos, 1980; Peskin, 1980; Preskill, 1981; Dimopoulos, Raby, and Kane, 1981; Ellis, Gaillard, Nanopoulos, and Sikivie, 1981)
23
I (p, ~Pz Pz ) = I 2 Tr( [t~, tz ]t, ) J
RpT 2
6m M(pT) (6.44)
where gp is related to the p —+vrm coupling constant gp
Pz
(ge/4vr=2. 98) by
If the condition (6.41) is not met, the lightest P3 s will be absolutely stable. In this model there are also 64 massive technivector
mesons, also listed in Table II. The 63 which lie in the adjoint representation of SU(8)i are called technirhos. They have the same SU(3), quantum numbers as the technipions, and have a common mass given up to QCD
corrections by (6.17) with F given by (6.38), '1/2 - -]/2
M (p T ) = 885 GeV/c 8 (6.43)
nf
(6.39) g p ge(3/N—)—, (6.45)
M(P3) =240 GeV/c 4 nf
N8
1/2 (6.40)
These estimates are of course specific to the color-SU(3) representations, to the SU(N)T& group, and to the flavor group (6.37).
If the weak hypercharge parameter Y [cf. Eq. (6,36)] satisfies
2F = ',—+integer, (6.41)
as it will for the canonical choice Y = —,, then the colortriplet technipions will decay as
P3~ ~ or (6.42)
2 GeV/c &M(P, P ') &40 GeV/c
the estimates are fairly independent of detailed assumptions. It is worth noting that the upper end of the range,
namely, 40 GeV/c, is considerably higher than the value of 14 CJeV/c sometimes quoted in the literature (Barbiellini et al., 1981). The lower value is the basis for experi
mental claims (Althoff et al. , 1983) that technicolor has been ruled out, a verdict we regard as premature. The color-triplet and color-octet technipions also receive electroweak and ETC contributions to their masses, but these are much smaller than the expected QCD contribution (Peskin, 1980; Preskill, 1981),
I /2
M(P3) =160 GeV/c nf
N8
4
p is the momentum of the technipions in the pT rest
frame, and the 4 are the SU(8) generators given in Table
II.
Like the pT of the minimal model, the p2 of the Farhi
Susskind model decays into m. TmT ( Wo8'o or Wozo) pairs, and will give rise to an enhancement in the cross section for pair production of gauge bosons. Because pz is
only half the mass of the pz of the minimal model, the
expected event rate is larger than that discussed in Sec.
VI.B. However, the greater width of p2 and the small
branching ratio for the 8'+8' decay reduce the effect
in the neutral channel to an enhancement of 20—25%%uo. We therefore illustrate in Fig. 180 the more prominent
enhancement in the O'+—Z channel, which will be somewhat easier to observe than the corresponding effect in the minimal model. Of more interest in the context of the Farhi-Susskind model is the role of the technirhos in producing other technipion species. The most important technirho for this purpose is pg', which has the quantum numbers of the gluon, and so can enhance technipion production through technivector meson dominance. We shall address this possibility below. The sixty-fourth technivector meson, coT, is a singlet under flavor SU(8), and so decays only into three techni
pions. It does not couple to the photon or Z or to two gluons, and therefore does not significantly enhance the
already rather small production of three technipions. We shall not discuss it further. The interactions of technipions with the SU(3),
SSU(2)1 U(1) i gauge bosons occur dynamically
through technifermion loops. At subenergies well below the characteristic technicolor scale, the technipions may be regarded as pointlike. Their couplings to gauge bosons
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


658 Eichten et a/. : Supercollider physics
TABLE III. Decay modes, branching ratios, and widths of neutral technirho mesons in the Farhi
Susskind model. Partial widths are computed from Eq. (6.44), with M(pT) =885 GeV/c, M(P3) =160
GeV/c, M(PS) =240 GeV/c . For each decay pz ~P&P&, the top number is the weight
I2Tr([ts, tc]t~ ) I and the second is the branching fraction.
Decay mode
p+p-,
PP+P P
pip 1+p —lp —1
P3P 3+P3P 3
pOpO'
P3P3+P3P 3
P8 P +P8 P+
P8 &T +PS ~T
P+~T+P-~T
7T+T7TT
3 2
0.34
3 2
0.34
1 2
0.16
1 2
0.16
6
0.18
1 2
0.15
3 2
0.33
1 2
0.15
1
6
0.05
1 2
0.14
Technirho P
2
0.50 2
0.50
Pl
3
0.12
2
0.13
0.50
3
0.10
1 2
0.15
P2
2
0.41
3 2
0.42
1
4
0.09
1
4
0.08
Total width (GeV)
440 460 550 550 490
—4
10
V
0
—5
10
DC
—6
10
III
pp ZW + ZW + anything
may therefore be calculated reliably, using well-known techniques of current algebra or effective Lagrangian methods (Chadha and Peskin, 1981a,1981b). At higher
subenergies ( ) 1 TeV), we shall improve this pointlike ap
proximation by using technirho dominance.
The production of a single-technipion P is governed by
its coupling to a pair of gauge bosons, BI and Bz. This coupling arises from a triangle (anomaly) graph analogous
to the one responsible for the decay n. ~yy. The ampli
tude for the PBIB2 coupling is (Dimopoulos, 1980; Dimopoulos, Raby, and Kane, 1981; Ellis et al. , 1981)
—7
10 SPB1B2 p 'v A p
PB1B2 2 ~ &PvAP~1 ~2P 1P 2
8m V2I (6.46)
—B
10 0. 4
I
0. 5
II II I
0. 6 0. 7 0. 8 0. 9 1 1. 1 Polr Moss (Te&/&')
where the triangle anomaly factor is
g1g2
s&a, &, = Tr(&IQI Q2I) .
FIG. 180. Mass spectrum of 8' +—Z pairs produced in pp col
lisions, according to the Farhi-Susskind model. The parton dis
tributions of Set 2 have been used. Both 8' +—and Z must
satisfy ~y ~ &1.5. The cross sections are shown with (solid lines) and without (dashed lines) the p2 enhancement.
Here gI and g2 are the gauge coupling constants, QI and
Q2 are the gauge charges, or generators, corresponding to
the gauge bosons, and Qz is the chiral SU(8) generator of
the technipion given in Table II. The contributions from different gauge boson helicity states are summed separate
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics
M(Bi)
I (B, +PBz—) = 96m
~PB )B2
8n v2F (6.48)
M(P)
1"(P~BiBz)=(1+5'zi ) 32m
~PB)B2
8n ~2F (6.49)
The PBiBz channel is of experimental interest only for neutral technipions, because the charged technipions are more easily produced in pairs. Therefore, we list in Table IV only the anomaly factors for neutrals. Models other than the Farhi-Susskind model yield similar results. One may infer from Table IV and Eq. (6.48) that the rates for the processes (Bjorken, 1976; Glashow, Nanopouios, aild Yildlz, 1978)
Zo~ZO (P or Po )
W +— W~ (P orP '), (6.50)
involving a virtual Z or W+— are 4 or 5 orders of magnitude smaller than the corresponding standard-model rates for the decays
z'~z'a,
(6.51)
Consequently if a neutral Higgs-type scalar is found at the levels discussed in Sec. IV.E,. the technicolor scenario would seem to be ruled out. More interesting from the experimental point of view
are the couplings of a single gauge boson to a pair of technipions. These provide access to nearly all the technipions, with cross sections that are generally quite large.
ly in the trace. These results lead to the following approximate decay rates valid when the product masses are negligible:
2
GFp (Mi~+MJ~)
I (P~fgfj )= C)q,
16m. (6.52)
where GF is the Fermi constant, p is the momentuin of
the products in the technipion rest frame, and C;J is a
color factor which is equal to 3 for the decay of a color singlet into quarks and 1 otherwise. The only possible ex
ception to the dominance of ff modes is the decay of P '
into two gluons, for which the partial width is
M(P ') N
r(P' gg)= 6m F
=14 eV 4
~ 2 r '3
M(P ')
1 GeV/c (6.53)
The BPP' couplings may be read off from an SU(3), SU(2)L U(1)i -invariant effective Lagrangia~
for the technipions (Peskin, 1980; Preskill, 1981; Lane, 1982). The results for the Farhi-Susskind model are given in Table V. A parenthetical note of caution about model dependence is in order here. In models more general than this one, mixing usually occurs among technipions with the same color and electric charge. Such mixing can occur
even in the Farhi-Susskind model between P and P ' and
Ps and P8'. The only entry in Table V that would be af
fected is that involving W —. The modification takes the form of model-dependent factors from the unitary matrices that diagonalize the technipion mass matrices. The cross section summed over all channels with the same color and charge should therefore still be given reliably by the couplings tabulated. The extended technicolor interaction couples technifermions to quarks and leptons, and so governs the decays of technipions into ordinary matter. For light color-singlet technipions, these are the dominant decay modes. If, like Higgs bosons, these couple to mass, the decays occur at a rate of approximately
TABLE IV. Anomaly factors S~~ z in the Farhi-Susskind model as defined in Eq. (6.47).
12
Vertex PB]B2
P'Z'Z'
pOZO+0
P'e+W
P gagb
pO'Z Oy
pO Z OZO
P'8 +8'
Ps0u rgb P8az gb P8Olgbg~ PSOlaggb P8az gb
SPBiB2
e (4N)/V 6
—e (2N/V 6)(2x~ —1) /(1 —x~)
e (N/V 6)(1—4x~)/[xg (1—xg )]'~ 0
g, (N/V 6)5,b
—e z(4N /3W6)
ez(4N/3V 6)[xg l(1 —xg )]'~z
—e (4N/3V 6)xg /(1 —xg ) 0
eg, X5,b
—eg, (N'/2)5, b (2x w 1)/[x w( 1 —x w) ]
g,2Nd, b, eg, (X/3)& b
—eg, (N/3)5, b[xg l(1 —xg )]'
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


660 Eichten et al. : Supercollider physics
oC
8
~~ X
QJ
0
ef
c&eD ~ E
~ 1H («($
05 ch
o ~ g~
C5
bQ hQ
ae O
rbH0Q
0S854 ~
'~ 1Q+I
I
Q
C6
.g~ 8
2
Pg Q0
0
rA Q
ct
0
rn O O
bQ
g
0
~0
tg
N
r 'g
O c0
Ch 0
~~~g+~I4 .~
~&
PVQ
aE5 c5
bQ c5 O
0$
O0
88
~ ph
C$
C$
«A
0
a5
hQ
e$
00
t5
M'cV M
~ ~ «~ «~
c t5
yO O
II
CQ
I
I
I
+
I
CL o~Q
eO O
F804 A„A„O„CL„lg„ Ig lg„ la„
+ +oe 0 tR 000 ~ K ~ K 0ch
0 0 ~+~
4„0
OOOOOOOO
+I
where the numerical estimate applies -for a, =0.2. This
becomes comparable to the rate for P '~bb for
M(P ')=40 GeV/c . It is also expected that heavy colored technipions decay predominantly to fermion pairs. The principal exception
to this rule would be the decay of Ps' into two gluons, for which the partial width is
5a, M(Ps')'
1(Ps' FF 4 (6.54)
Because of the anticipated dominance of ff decay
modes, it is of great importance to know what the extended technicolor interactions are. It is just in this regard that the existing models, including that of Farhi and Susskind, cannot be relied upon (Lane, 1982). One statement that is known to be generally-true about technipion couplings to light fermions is that they are parity violating (Eichten and Lane, 1980), and probably CP violating as well (Eichten, Lane, and Preskill, 1980). This fact may lead to many interesting investigations if technipions are ever found. We put aside such questions and focus on the initial search. According to the conventional wisdom, which is inspired by analogy with the minimal electroweak model, the technipions couple essentially to fermion mass. Bearing in mind that this tendency to couple to mass can be evaded even in the case that there are two or more elementary Higgs doublets, we list in Table VI the expected major decay modes of technipions. In the interest of brevity, we shall base most of our discussion of signals on this most obvious possibility.
D. Single production of technipions
The production of single technipions is in many respects analogous to the production of Higgs bosons
treated in Secs. IV.D and IV.E. It may proceed by twogluon fusion or by quark-antiquark fusion. The most important process is the production of the neutral techni
pions P ' and Ps' in gluon-gluon fusion, which leads to
equal cross sections in p —p collisions. Ignoring any mix
ing with P and Ps, we may write the differential cross sections as [compare (4.86)]
Tech nipion
p+
pO po'
(if unstable)
p+ p0 po'
Principal decay modes
tb, cb, cs, ~+v, bb, cc,~+~ bb;cc, r+r;gg
t~ )tv~)b~+). . .
or tt, tb, . . .
(tb)g (tt)8 (tt)8, gg
TABLE VI. Principal decay modes of technipions if Pfqf2
couplings are proportional to fermion mass.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 661
0 (ah~P'+anything) = 2 rfs (x„M )
'Ir I (P ~Ra) (aI 2
8M O
0. 9
xfs '(xb, M ),
with
xb v r—e J', 
where we have abbreviated M (P') as M and as usual
x. =V ~e&
(6.55)
(6.56}
0. 8
0. 7
Kl
0. 6
0. 4
0. 2
v=M /s . (6.57) 0. 1
The partial widths I (P'~gg) are given in (6.53) and (6.54).
The differential cross section for P ' production at
y=O is shown as a function of'the technipion inass in Fig. 181. According to (6.52} and (6.53), the principal decays will be into
(6.58)
with branching ratios indicated in Fig. 182. Comparing
with the two-jet mass spectra shown in Figs. 90—94, we
see that there is no hope of finding Po' as a narrow peak in the two-jet invariant mass distribution. The background from bb pairs, estimated using (5.17) and (5.18), is shown in Fig. 183. It is 3 orders of magnitude larger than
the anticipated signal. The background to the r+v
I II I II I II
i0 15 20 25 30 35 40 45 50 55 60
Mass (GeV/c )
FIG. 182. Apyroximate branching ratios for P decay. In Eq.
(6.53) me choose X =4 and use the running coupling a, (Mp).
mode is the Drell-Yan process, for which the appropriate cross sections have been given in Figs. 108 and 109. Even wh'en the small ( -2%%uo) branching ratio into ~ pairs is taken into account, the signal is ap'proximately equal to or an
order of magnitude larger than the background. The signal-to-background ratio is crucially dep'endent upon the experimental resolution in the invariant mass of the
pair. It seems questionable that taus can be identified with high efficiency and measured with sufficient precision to make this a useful signal. The differential cross section for color-octet (Ps') technipion production at y=O is shown as a function of the
1D
20
40
70 '100 10
LO
V
C
C3 10
XJ
b
1D-1 io
ol
-p p M P + anythtng
10 I I I I I I I I I I
15 80 25 30 35 40 45 SO SS 60
Mass (GeV/c*)
FIG. 181. Differential cross section for production of the
color-singlet technipion P at y =0 in pp or pp collisions, ac
cording to the parton distributions of Set 2.
40
20
IIII I
10 30 50 60 70
Mass (GeV/c*)
FIG. 183. Cross section der/d~ dy ~ ~ 0 for the production of
bb pairs in pp collisions, according to the parton distributions of
Set 2. V s =2, 10, 20, 40, 70, and 100 TeV.
Rev. Mod. Phys. , Vol. 66, No. 4, October 1984


Eichten et af.: Supercollider physics
technipion mass in Fig. 184. The dominant decay modes will be
gg (6.59)
The expected branching ratios depend upon the top quark mass. Representative estimates are shown in Fig. 185. The background expected from tt production by conventional mechanisms is plotted in Fig. 158, for a top quark
mass of 30 GeV/c . When the branching ratios are taken into account, the signal and background are roughly comparable, and the expected number of events is quite large at supercollider energies. The signal-to-background ratio
improves somewhat with increasing P8' mass. The main issues for detection are the identification of t quarks and the resolution in invariant mass of the reconstructed pairs. This is an appropriate topic for Monte Carlo studies. In the two-gluon channel, the signal will be comparable
to the tt signal or (for large P8' masses) somewhat larger. The expected background, which may be judged from
Figs. 90—94, is very large compared to the signal except
at the highest P8' masses considered.
To sum up, the neutral technipions P ' and P8' will be produced copiously in high-luminosity multi-TeV colliders. However, within the conventional scenario for their decays, detection requires the ability to identify and measure top quarks and tau leptons with high efficiency and high precision. Extraction of a convincing signal will mightily test experimental technique.
E. Pair production of technipions
and
We now discuss the production of pairs of color-singlet technipions through the chains
p +—p —+ S'+—+anything
(6.60)
C() 10
II
0
—1
40
—8
10
10-3 0.8 0. 3 0.4 0.5 0. 6
1
p —p~Z +anything
p+p— (6.61)
as well as the production of pairs of color-triplet or color-octet technipions in gg and qq collisions.
According to the mass estimates (6.39), both charged and neutral color-singlet technipions are expected to be lighter than 40 GeV/c . Consequently, both species should be produced in intermediate boson decays (Lane, 1982,1984). From the couplings given in Table V, we may estimate the branching ratios in the Farhi-Susskind model to be
Mass (Tev/g*)
FIG. 184. Differential cross section for production of the
I
color-octet technipion P8 at y =0 in pp or pp collisions, accord
ing to the parton distributions of Set 2. The expected mass, according to (6.40), is approximately 240 GeV/c .
r( w-+
I ( 8' +—~all)
(Mo —M+) 3/2
1— Mg
3/2
(Mp+M+ )
AM@ 1— Mg
48xwl ( W +—~all)
3/2
(M, +M+)'
=0.02 1— Mg
(Mo —M+ ) 3/2
1— M~ (6.62)
r(z' p+p-)
I (Z all)
aMz(1 —2xw) 1
=0.01 4M
1—Mz
4M'
Mz
48xw(1 —xw)I (Z ~all)
(6.63)
1
where xw — —sin Ow. The estimate (6.63) for the techni
pion branching ratio of X is model independent. The es
timate (6.62) for the 8' branching ratio may be modified by mixing angles in more complicated models. The very large samples of intermediate bosons anticipated in high
energy pp and pp collisions (compare Figs. 110—112 and
114—116) may make possible the study of these rare decays. The prospects have been considered by Kagan
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 663
(1982) and Lane (1982). The elementary processes for pair-production of colored technipions are depicted in Fig. 186. The differential cross sections for neutral channels are and
22
(qq~PP) = T(R)P2 ~ X ~
2(1 —z2), (6.64)
dt
do' 2m a, T(R)
(gg —+PP) =
dt s2
T(R)
d (R) (1 —2V+2V')+ —',, p'z'( ~ X ~
' —2VReX+2V') (6.65)
where z = cos8 measures the c.m. scattering angle,
P2=1 4M(—P) /s,
I
or
P +P — POPO +PO tPO t (6.73)
2
1 —Pz
and the ps' enhancement factor is
M(ps')
X= M(ps') —s —iM(p8')I (s )
(6.67)
(6.68)
occur with equal cross sections. As is the case for the pair production of heavy quarks, the gluon fusion mechanism is the more important at collider energies, so that the cross sections in pp and pp col
lisions are nearly equal. The integrated cross section for the reaction
where the energy-dependent width of ps' is
M(po, )r(s)= " [P',e(P, )+3P',e(P, )] . (6.69)
The color factors are
for P,
T(R)= .
3 for Ps (6.70)
3 for P3
d(R)=. 8 for Ps. (6.71)
P'P' P 'P P P, P'P' ' (6.72)
In writing (6.64) and (6.65) we have summed over all charges and colors. The individual charge states
pp ~P3P3 +anything, (6.74)
summed over the charge states (6.72), is shown as a function of M(P3) in Fig. 187 with and without the p8'
enhancement. For the purposes of this calculation, we adopted the canonical value (6.43) M(ps')=885 GeV/c of the technirho mass and evaluated the mass-dependent technirho width, using (6.44) with M(P8) fixed at its
nominal value of 240 GeV/c, as given by (6.40). The cross sections are substantial. The same cross sections are shown in Fig. 188 for technipions satisfying the rapidity
cut ~ y ~ &1.5. We have also computed these cross sec
tions using the parton distributions of Set 1; they differ by no more than 10%%uo. Comparing Figs. 187 and 188, we find that the degree of ps' enhancement is not much affected by the rapidity cuts. The enhancement is generally not so dramatic that
measurement of the P3P3 production rate would confirm
or deny the existence of ps', much less determine its pa
O
0. 9
0. 8
0. 7
Kl
m& 70 GeV/c*
y P p/
g
'v
)IO
(
IO
0. 4
0. 3 V/c'
0. l.
0. 12
II
0. 2
I II
0.28 0.36 0.44 Mass (TeV/c*)
FICx. 185. Branching fractions for P8 ~tt. The remaining decays are into the two-gluon channel.
FICx. 186. Feynman graphs for the production of pairs of colored technipions. The curly lines are gluons, solid lines are quarks, and dashed lines are technipions. The graphs with schannel gluons include the p8 enhancement.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


664 Eichten et al. : Supercollider physics
rameters. For example, at vs =40 TeV, the P3P3 cross
section (with rapidity cuts) is enhanced by a factor of 1.3
at the canonical technipion mass, M(P3)=160 GeV/c
(6.40), by a factor of 2 at M(P3) =280 GeV/c, and by a
factor of 14 at M(P3)=400 GeV/c .
If the technipions are stable, which will be the case if (6,41) is not satisfied, the signatures should be quite striking and essentially background free. Each event will appear as a pair of extremely narrow jets consisting of the very massive P3 core (plus a quark or antiquark to neutralize its color), together with relatively soft qq pairs and
gluons. ' The decay of unstable technipions into
q +I+. . . should also provide a characteristic signature:
a jet and an isolated lepton on each side of the beam. In this case the only comparable conventional background would be from the pair production of heavy quarks, with the subsequent decay
Q~qW
(6.75)
10
10
10
—4
10
0. 12 0. 2 '0. 28 0.36 0. 44
For such events one expects equal numbers of electrons, muons, and taus. In contrast, the technipion decays are
expected to favor taus. We conclude that the identification of P3P3 pall production at supercollider energies should be. possible even
at quite modest luminosities ( 1 Wdt&10 cm ) for
technipions of the canonical mass. Reconstruction of an invariant mass peak may be quite demanding because of
the difficulty of measuring the momenta of heavy quarks and leptons. We turn next to the pair production of octet technipions. The integrated cross section for the reaction
Mass (Te~/c~)
FIG. 187. Integrated cross section for the production of P3P3 pairs in pp collisions, according to the parton distributions of
Set 2. All charge states are summed. The cross sections are shown with (solid lines) and without (dashed lines) the technirho (ps) enhancement of Eq. (6.68). The technirho parameters are given in the text. The canonical value of the technipion Inass is
M(P )=160 GeV/c .
10
pp ~P8P8 +anything (6.76)
is plotted in Fig. 189 with and without the ps' enhance
ment. These are typically —15 times the cross sections for color-triplet technipion production, because of the larger color factors in (6.65), and comparable to the cross sections for single-Ps' production. The effect of the re
striction ~y ~ &1.5 on the technipion rapidities is illus
trated in Fig. 190. In this case, we have computed the mass-dependent ps' width, using (6.44) with M(P3) fixed
at its nominal value (6.40) of 160 GeV/c . The technirho enhancement is less effective in the octet technipion channel because of the large color factor in the first term in (6.65). The expected decays of octet technipions are
P8+ —+tb,
—2
10
10
and
P8~tt,
0 (6.77)
Time-of-flight methods for heavy-particle detection have been explored by Baltay et al. (1982).
—4
10'
III
0. 2
II I I II I
0. 12 0, 28 0. 36 0. 44
Moss (Tev/c*)
FIG. 188. Cross section for the production of P3P3 pairs in pp
collisions. Rapidities of the technipions must satisfy ~ y ~ & 1.5.
The cross sections are shown with (solid lines) and without (dashed lines) the ps enhancement of Eq. (6.68). Parameters are
as in Fig. 187.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et af.: Supercoliider physics 665
0, tt (6.59)
io
—1
10
10-2
with branching fractions given earlier in Fig. 185. The signature for the Ps+Ps channel is therefore tb on one
side of the beam and tb on the other. If the heavy flavors can be tagged with high efficiency, we know of no signifi
cant conventional backgrounds. If it is necessary to rely on the four-jet signal, the @CD background must be considered. At present, this can neither be calculated nor reliably estimated. Similar conclusions apply for the neutral octet technipions. The charged-octet technipion can also decay by means of the triangle anomaly mechanism [compare Eqs. (6.46) and (6.47)] into two gauge bosons,
I's+ ~g W'+ . (6.78)
The estimates (6.49) and (6.52) of the decay rate would suggest that
10-3 0.36 0.44 Mass (Tey/c~)
r(p+ gW+)
r(p+ tb) 5 10 (6.79)
FIG. 189. integrated cross section for the production of P8P8 pairs in pp collisions, according to the parton distributions of
Set 2. Both charge states are summed. The cross sections are shown with (solid lines) and without (dashed lines) the technirho (pa) enhancement of Eq. (6.68). The technirho parameters are given in the text. The canonical value of the technipion mass is
m(P, ) =240 Gene'.
The signal of a jet and an intermediate boson opposite two
jets or of a jet and an intermediate boson should be rather characteristic. Again, the pair production of heavy
quarks is a background to the (g8'+)(gS' ) signal.
F. Summary
2
10
—1
10
—3
10 0. 12 0.2 0.28 0.36 0.44 Mass (TeV/c )
FICr. 190. Cross section for the production of P8P8 pairs in pp
collisions. Rapidities of the technipions must satisfy y &1.5.
The cross sections are shown with (solid lines) and without (dashed lines) the p8 enhancement of Eq. (6.68). Parameters are
as in Fig. 189.
If the technicolor scenario correctly describes the
breakdown of the electroweak gauge symmetry, there will
be a number of spinless technipions, all with masses much smaller than the TC scale of about 1 TeV. We have analyzed the simple but, we believe, representative model
of Farhi and Susskind (1979), in which color-singlet technipions lie between 5 and 40 CieV/c and colored technipions occur between 100 and 300 CreV/c . Other models will have similar spectra. The couplings of technipions to the SU(3), SU(2)L,
U(1)r gauge bosons are reliably known, so the production cross sections can be estimated with confidence. The technipion couplings to quarks and leptons are not known with comparable certainty. All our comments about the signals for technipion production must therefore be regarded as tentative. For any hypothesis about technipion decay, careful Monte Carlo studies will be required to ascertain morc accurately the signal and background levels. In the absence
of such information, we have tried to be sensibly conservative in estimating the capabilities of multi-TeV hadron
colliders to search for signs of technicolor. A rough ap
praisal of these capabilities is given in Table VII, where we have collected the minimum effectiue luminosities required for the observation of technihadrons. In constructing the table, we have required that for a given charge state, the enhancement consist of at least 25 events, and that the signal represent a five-standarddeviation excess over background in the rapidity interval
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


666 Eichten et aj'. : Supercollider physics
TABLE VII. Minimum effective integrated luminosities in cm ~ required to establish signs of tech
nicolor in p —p colliders. To arrive at the required integrated luminosities, divide by the efficiencies c;
to identify and adequately measure the products.
Collider energy
Channel
2 TeV 5'P 10 TeV 20 TeV 40 TeV 100 TeV
Minimal model:
pT —+ Wp Wp
pT —+Wp Z
Farhi-Susskind model:
P'~~+v. 
P8'~tt (240 GeV/c ) P P (160 GeV/c ) (400 GeV/c ) P8P8(240 GeV/c ) (400 GeV/c )
pT —+WOZ
5 X 1o'6
2X10" 2X10"
lp38
8 X 10"
7&&10'4
2X10"
lp38
2~ 10"
2 && 1036
2&& 10
3.4X 10 1.6&&10"
3 ~1035 3 ~1034
4~10"
2~10"
5 &&10'4 4X 1035
7~10
1~ 10" 6~1038
2~1035
1p34 2&& 10" 4&&1036
2~10'4 10"
3 0&10
6 + lp38 2~ ]038
1p35 3 X1033 7~1034
lp36 7& 10
3 &&1034
1.5 &(10
—1.5 & y & 1.5. The effective luminosities quoted must be
adjusted for the finite efficiency to identify and measure the decay products. We have used the branching ratios of
Fig. 182 for P ~~+&—,and Fig. 185 for P8~tt, with
m, =30 GeV/c, and have assumed that all P3's produced in the rapidity bin are detectable. We remind the reader one last time that we have assumed the conventional wisdom for the decay modes of these particles, and that the exploitation of some of these decay modes will require advances in detector technology. With that final caveat,
we conclude that a 40-TeV p —p collider with a luminosity
of at least 10 cm will be able to confirm or rule out technicolor.
VII. SUPERSYMMETRY
The fermion-boson connection known as supersymmetry (Gol'fand and Likhtman, 1971; Volkov and Akulov, 1973; Wess and Zumino, 1974a,1974b, 1974c; Salarn and Strathdee, 1974a, 1974b; Fayet and Ferrara, 1977; Wess and Bagger, 1983) is a far-reaching idea which may play a role in the resolution of the Higgs problem. It is natural to hope that supersymmetry might reduce or even eliminate the freedom surrounding fermions and scalars in existing theories by linking the fermions to the vectors and the scalars to the fermions. We have already discussed in Secs. IV and VI the naturalness problem of the Higgs sector of the standard
SU(2)L, SU(1)~ electroweak theory, which has been posed
most sharply by 't Hooft (1980). Technicolor provides one possible solution, with the proposal that the scalars are composite particles, with the compositeness scale a
few times the electroweak scale. The consequences were elaborated in Sec. VI. Supersymmetry, in contrast, provides the only natural framework in which to formulate spontaneously broken gauge theories involving elementary scalars. The implications of the supersymmetry alterna
tive for experimentation at supercollider energies will be
explored in this section.
In the minimal (%=1) supersymmetric theory, every
particle is related to a superpartner that differs by —' , unit of spin and otherwise carries identical quantum numbers. Among the known particles there are no satisfactory candidates for pairs related by supersymmetry. Consequently we must anticipate doubling the spectrum by associating
to every known particle a new superpartner. If supersymmetry were exact, each particle would be degenerate in mass with its superpartner. This is plainly not the case. For theories in which supersymmetry is broken, the mass degeneracy is lifted. The masses acquired by the super
partners are highly model dependent. However, if super-, symmetry is to contribute to a resolution of the hierarchy problem (Gildener, 1976; Weinberg, 1979b), the mass splittings should not greatly exceed the electroweak scale. This suggests that the low-energy artifacts of supersymrnetry, including the superpartners, should occur on a
scale of —1 TeV or below. No superpartners. have yet been found. However, some useful bounds on superpartner masses have been derived from studies of electron-positron annihilations, from hadronic beam-dump experiments, and from cosmological constraints. The current experimental situation has been
summarized by Savoy-Navarro (1984), Dawson, Eichten, and Quigg (1984), and Haber and Kane (1984). In addi
tion, Dawson et al. have presented a collection of all the relevant formulas for the production of superpartners in hadron collisions. We adopt their conventions and notation. This section is organized as follows. In Sec. VII.A we review the expectations for the superparticle spectrum in a minimal supersymmetric theory and summarize the elementary cross sections for superpartner production. Section VII.B contains the estimated rates for the production of superpartners of quarks and gluons in high-energy p +—p
collisions, and a discussion of experimental signatures. A
similar treatment of the supersymmetric partners of elec
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten ef af.: Supercollider physics 667
troweak gauge bosons and leptons takes up Sec. VII.C. Some general conclusions about the prospects for the observation of superpartners at supercollider energies appear
in Sec. VII.D.
A. Superpartner spectrum and elementary
cross sections
In this paper we shall examine the simplest (X= 1) su
persymmetric extension of the SU(3), SU(2)I. SU(1)z
model of the strong and electroweak interactions. To every known quark or lepton we associate a new scalar superpartner to form a chiral supermultiplet. Similarly, we group a gauge fermion ("gaugino") with each of the gauge bosons of the standard model to form a vector supermultiplet. The couplings in the Lagrangian are then completely specified by the gauge symmetry and the supersymmetry algebra (Wess and Bagger, 1983). Some theories in which supersymmetry is respected at low energies naturally possess a global U(1) variance, usually called R invariance (Fayet, 1975; Salam and Strathdee, 1975; Fayet and Ferrara, 1977). In such theories there is, in addition to the standard quantum numbers, a new fernilonlc quantum number R associated with the U(1) symmetry. Quantum number assignments for the conventional particles and their supersymmetric partners are given in Table VIII (from Dawson et al. , 1984), where
7=+1 is a chirality index. R invariance is undoubtedly broken by the vacuum expectation values of the Higgs scalars, which break the electroweak SU(2)L, 13U(1)~ sym
metry and endow the 8' — and Z with masses. The phenomenological consequences of various possibilities for residual or broken R invariance have been analyzed by
Farrar and Weinberg (1983). In writing cross sections, we have assumed that no continuous R invariance remains. This is generally required to give Majorana masses to the gauginos. We do not choose any particular model of supersymmetry breaking or make any explicit assumptions about the Higgs structure of the theory. However, in any supersymmetric theory at least two scalar doublets are required to give masses to the fermions with weak isospin of both
I
3 —+ 2 As a result, there will be charged scalars in addition to the familiar neutral Higgs boson. The signatures of the charged scalars would resemble those of the techni
pions I'+— discussed in Sec. VI. In general, mixing may
occur between the gauge fermions associated with W~,
Z, and y and supersymmetric partners of the Higgs bo
sons (Ellis et al., 1983; Frere and Kane, 1983), so that the
mass eigenstates are linear combinations of the two species. This would introduce mixing angles in the electroweak gaugino sector. In our calculations we ignore such mixing, as well as the direct production of Higgsinos. The latter approximation would seem quite justified in hadron-hadron collisions because of the small Yukawa couplings of Higgsinos to light quarks. Our discussion can easily be extended to include the appropriate mixing angles. These issues are treated more fully by Dawson et al. (1984). When global supersymmetry is spontaneously broken, a massless Cxoldstone fermion, the Goldstino, appears. Because the couplings of the Goldstino to quarks and gluons are quite small, we do not calculate cross sections for its direct production. The Cxoldstino will, however, appear as a possible decay product of the other superparticles. In locally supersymmetric
models, the Goldstino becomes the helicity + —' , com
TABLE VIII. Supersymmetric partners of SU(3), SU(2)L, U(1)~ particles.
y O' —,Z
r
-+,z'
Particle
gluon gluino
photon photino
intermediate bosons
wino, zino
quark
squark
electron
selectron neutrino
sneutrino
Spin
1 2
1 2 1 2
0
1 2
1 2
Color Charge
0 0
+1,0 +1,0
21 3~ 3 21 s3
R number
0
0
0
Higgs bosons
H+ H'
H H +1,0
Higgsinos
r
H+ H'
H' H- 1
2 +1,0
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


668 Eichten et al. : Supercollider physics
ponents of the massive, spin- ',—gravitino (Deser and Zumino, 1976). In such models, the photino is often the lightest superpartner. For the remainder of this section, Goldstino will refer to either case. The usual Yukawa couplings of scalars to quarks or leptons generalize in a supersymmetric theory to include Higgs-squark and Higgs-slepton couplings, as well as Higgsino-quark-squark and Higgsino-lepton-slepton transitions. Just as there is a Kobayashi-Maskawa matrix which mixes quark flavors and introduces a CP-violating phase, so, too, will there be mixing matrices in the quarksquark and squark-squark interactions. Mixing may also occur in principle in the lepton-slepton and sleptonslepton interactions. While there is no general theoretical reason for the mixing angles to be small, the requirement that a supersymmetric Glashow-Eliopoulos-Maiani (1970) mechanism operate to suppress flavor-changing neutral currents places some restrictions on squark mass split
I
tings and on mixing angles. For an up-to-date assessment of these constraints, see Baulieu, Kaplan, and Fayet (1984). For simplicity, we will assume that there is no mixing outside the quark-quark sector. As a result, each quark (or lepton) of given chirality will couple to a single squark (or slepton) flavor. The general case is.treated in Dawson et al. (1984). Once we have stated the ground rules, it is straightforward to calculate the elementary cross sections for the production of superparticles in collisions of quarks and gluons. We summarize the results of Dawson et al. (1984).
1. Gaugino pair production
The differential cross section for the production of two gauge fermions in quark-antiquark collisions is given by
(t m])(t ——m2) (u —m])(u —m2)
22
+A, +A„
(t M, ) — (u —Mg)
(t —m&)(t —m&)+m&m2s m~rn2s
A~u
(s M, )(t M—, ) — (t —M, )(u —M„)
+As~
(u —m f )(u —m 2)+m ~m2s
(s —M, )(u —M„)
(t —m f)(t —m2)+(u —m f)(u —mz)+2m~mzs
(qq '~gauginos) = A,
dt S (s —M, )
(7.1)
where m& and m2 are the masses of the produced gauginos, and M„M„and M„are the masses of the particles ex
changed in the s, t, and u channels, respectively. The coefficients A„are collected in Table IX for all possible pairs of gauginos. The total cross section is
r
o(qq'~gaugmos)= I2s +sf6m&m2 —(mf+mz)] —(m& —m2) I
(1+I)s 3(s —M, )
r r ~~~i~~2
p'+ (6,)+5,2)A, + M, +rn fm z +M, (s m& —m z )
22
A„2 s+m &+m2
W M, — +(h, ~b,,2+m~rn2s)A, + (t~u) '
s —M 2
s+Ag)++„2 (7.2)
The quantity 1/(1 + I) is a symmetry factor for identical particles. I= 1 for identical gauginos g g, y y, and Z Z; in all
other cases, I=O. We have also introduced the convenient quantities
and
[s (ml +m2)'1'"[s —(mi —m2)'1'
22
A~; =M~ —m;,
(7.3)
(7.4)
s+b~ i+6~2 —W
A, = ln s+ h~ i+ A~g+ W (7.5)
Rev. Mod. Phys. , Vol. 56, No. 4, October 3984


Eichten et 8/. : Supercollider physics
TABLE IX. Coefficients' for the reaction q;q~ —+gauginol + gaugino2.
Exchanged Por ticle 90uginol gaugino2
Z
0
0
0
At
2a eq qq
8as aeq2
9 qq
L2+ R2
12xw 1- x w
Au
A,
A)
A,
Ast
0
0
Asu
0
4tu
-24
-24t
-2 At
Z -$41
q q 0 9xw 1 xw 4) 0 0 -2At
ANO q Z
8a 2
Sqq'
eq (Lq+R&)
eq+ (1- z—)
(L +R )
32 as
27 '4
12x w
At 8as qq' Ast
ae Lq aa Lq
eq + ~* —eq+ M~
Zx„(1- s*) ~"w 2x„(1- s )
xB„B„
8as qq
+
W L2
WW
a Lq
6xw2 8,„8„
Lq'Lq 12xw' {1-xw
xS
q~/ q 8,„8„ 2 2.
6x z ju Bqd 6x w Oqu Ofi'4 3x w qu qd
Q eq
Bx~ QU 841 .3Sx,w„S...
0 2as a 8,„8„ 2asa
gxw Squ Sqd 0 0
-4 usa 9xw
x8,„8,g
'Here x~ ——sin~8~. The neutral-current couplings are defined in Eqs. (7.22) and (7.23).
The production of gluino pairs also occurs in gluon-gluon collisions, with the differential cross section
9~~2 2(t —m-)(u —m-)
dt-(gg Fg)= ' ' +
4A. 2
(t mg)(u— mg } -2mg2(t—+mg2)
(t —m-)2
(t —m-)(6' —m-) +m-(u —t )
A,
s(t —mg-)
+ [t~u]
m-(s —4m-g)
+~ 2 2
(t —m )(u —mg-)
(7.6)
where m- is the gluino mass. An elementary integration gives the total cross section
g g)= 3~&s 4m
'2 31+
4s s
4m4
sA. 2
r s+W
ln s —P'
17m '
s
' s (7.7)
2. Associated production of squarks and gauginos
The differential cross section for the production of squarks and gauginos in collisions of quarks and gluons is
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


670 Eichten et al. : Supercollider physics
do (p t )—s+2p (m; t)

(gqt ~gaugino+qt ) = Bs „+Bt
dt" (t. p2)2
B„(u—p )(u+m; ) 8„[(s—m;+p )(t —m; ) —p s]
+ 22 +
(u —mt ) s(t p)
s(u+p )+2(m; —p )(p —u)
+&su $(u —mt )
A.
(m; —t)(t+2u+p )+(t —p )(s+2t —2m; )+(u —p )(t+p +2m; )
+8,„ 2(t —p )(u —m; )
(7 &)
where p is the mass of the gauge fermion and m; is the mass of the squark. The coefficients 8„ for each of the final
states are tabulated in Table X. Upon integration we obtain the total cross section
o(gq; ~gaugino+q; ) = 8, (1 b/s )+Bt[2 b—&/s+(s+2p2)A]
S
+8„[W(1+2A/s)+(3m; —p, )A]+8„[W(1—6/s)+(m; —b, /s)A]
+8,„[P'(1—2b, /s)+(p +m; —2b, /s)A]
+8,„I —[mt +p +2(m; —p )/s]A+[ —2mt + 2(mt —p )/s]A —WI (7.9)
where
22
6= f7' —P (7.10)
(7.11)
and
b, —s —W
A=ln b, —s+W (7.12)
3. Squark pair production
The production of pairs of squarks in hadron collisions can occur in quark-quark, quark-antiquark, or gluon-gluon collisions. For the first two cases we shall include only the gluino exchange contributions. The differential cross sec
TABLE X. Coefficients for the reaction gq;~gaugino+ qJ.
Exchanged partic1e Gaugino B,„ B,„
asaeq
lJ 0 B, 0 —B,
5;„5Jd
12x gr asa Lq ++q
22
24xp 1 —xg 4a, 9
' 5;J
0
0
a,25;J 4a, 5;J
0
0
'25; ~
18
0
'Here x~ ——sin 0~. The neutral-current couplings are defined in Eqs. (7.22) and (7.23).
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984


Eichten et ai.: Supercollider physics 671
tions for these cases are
4m',2 9s2
(q;qj ~q;qJ. ) = (t m ;—)(t m ~—)+s t (u —m; }(u —m )+s u
~~
(t —m )2 (u —m-)
sm- 2sm-g
5"— 5"
(t m—-) (u —m-) 3(t —m-)(u —m-) (7.13)
and
yg 4m',
9
(q;qj ~q;q J ) = ~
ut —m m.J
s
sA2
2 + ~ 22 +
g
3 t —m- (t —m-g)
m-s
(t —m-) (7.14)
1 2m t 2m u 4m
22, ~ 22 2 ~ 2
(t —m) (u —m) (t —m)(u —m)
where m is the common mass of the produced squarks. The total cross sections are easily computed as
where m; and mj are the masses of the produced squarks and m- is the gluino mass. In the case of gluon-gluon col
g
lisions, the differential cross section is given by
do, ~~s 7 3(u —t)
dt s 48 16s
-(gg q;q*;}= „+ (7.15)
4m+,
o(q;qj —+q;qJ. ) = 9$ 2
Wsms
—2P' —(s+ 6„+b,„)A,+ 1+5(J. h„bq +sms
A.
1 sm
+ —5" g
s+ 6„+E,J.
A, +5;,(t~u) (7.16}
4m.a,
o(q;qj ~q;q J ) = 27$
W(s+b„;+5~} 2(b.„bq+mss}.
V ~2+
ss s
asm
+3 —2W —(s+b,„+h„)A,+ sm-+ AgA,) (7.17}
CX 2
q;q';)= 3s m ln (7.18)
We shall also require the cross sections for the production of pairs of the supersymmetric partners of leptons in
quark-antiquark collisions. These reactions proceed by the exchange of photons and Z 's in the direct channel. The differential cross section is
4~~2 2 2 eqet(Lq+Rq)(L1+Rl } (Lq+Rq)(Lt +Rt )
dt 3s 8xw(1 —xw)(1 —Mz/s) 64xw(1 —xw) (1 —Mz/s)
where m& is the slepton mass, and the total cross section is
eqet(Lq+Rq)(Lt+R() (Lq+Rq)(Lt +Rt )
( — I ie) 2 2+
9s 8xw(1 —xw) (1—Mz/s) 64xw(1 —xw) (1—Mz/s)
4
u t —m-I
s (7.19)
(7.20)
Here the chiral neutral current couplings are
I.f —~~ —2efx~,
(3)
(7.21)
I
where q.f ' is twice the (left-handed} weak isospin I3 of
fermion f, ef is the fermion charge in units of the proton
charge, and
Rf ———2efxw ~ x~ ——sin 28~ (7.22)
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


672 EIchten et g) . SUpe ' er physics
is the weak m' ' eter. After th
mixing param
tions.
e task ' 'n
o estimatin
ese rel' 'ng supercollider cross
B. Prroduction and detectio interacting super partners
etection of strongly
We noow discuss thee rraates expected f uction in
e or suar
hg - Sy
and
p odiictloil arises iii
ition, upon the s
channel a " e squark mass th in
and u-channe
at appears g
a ive case of e
The cross
1 equa squark
e cross sections for lui 0 pp col
u o uction in
of the commo
eV are s
ese estimates a
mon squark and re based o th et . Here and
n e parton distri
require that h
tribu
a t e supe art
1S discussion
ergies. For
uite ar e a
s —40 'IeV
greeaat er than the v e
t e cross
energy su
n typical models of 1
e cross sections for pr
ries, production i'nn pp collisions
es etw an pp cross section
unim
gg po
ons re ect
h ec ions will be rather in
d th tq ese results to
gluino m
dit b tio ofS
Co ious proo o, o g
o more than ui os therefor olllders 1n th n TeV.
e ener ra
SS
duction rat
i we have
w g uinos m
ra es.
1 dh is survey of r
Associated
o pro
d production of sq gm o o 'd
g
do k, h
h f g1 po
g own
ae ro
up and d
q production.
m or squar
e the doominant
q
parable, .associated prooduction will
r and gluino
o a cross section f uinos is given b th
y e clem
qd, gq„, and gqg final
10 "$:=
10
J$:
A = 290 Me&
10' I
10
10 Xil-):
PP
29O Mev
10
0.25
\
'L
1
~C10
100
10
. 20 w10
4,
10 I I I I 'I. I
1.25 Gluin
2 1.75
Uino Mass (TsVj'c' PP ~gg + anything
TV d he 1c is set equal to the ggl uIno mass.
+PL
\\
lll
10
10
0.25
I
0.75
1.I25
1.I75
Glu&na Mass (TeV/'c~)
ross sections for t
a ' guino m, i
unction of l ' e reaction
e . Cutsa p
ing to the e ers are as in ig. 191.
Rev. Mod. Phys. V, 4
s., oI. 56, No.
s, . 4, October 1984


Eichten et al. : Supercollider physics 673
4
10
10 3 '.
10 2
5-JiIh;
10
III
PP - 99
4
10
10 i=
2
10 lIl
A = 290 M~v
10
10
10 0.25
I
0.75 1.25 Mass (TeV/c')
1.I75
\
\l\. y
. 40 ~- 20 10
~ . 100
FIG. 193. Cross sections for the reaction pp~gg+ anything
as a function of gluino mass, according to the parton distributions of Set 2. Cuts are as in Fig. 191, but the squark mass is chosen as 0.5 TeV/c .
states, then the cross sections are equal in pp and pp col
lisions. The total cross section is shown in Fig. 195 for the case of equal squark and gluino masses and the parton distributions of Set 2. We next consider the pair production of squarks in p ~p
collisions. In these considerations we shall assume for simplicity that the scalar partners of left- and righthanded quarks are degenerate in mass but distinguishable,
10
i. ' 10 2 lj. ;
-1 4 '1 \
A = 200 Mev
10
10
10
0.25
l
I &I
0.75
I
'1.25
1.I75 Gluino Mass (Tev/c*)
FICx. 194. Cross sections for the reaction pp~gg+ anything
as a function of gluino mass, according to the parton distribu
tions of Set 1. Cuts and parameters are as in Fig. 191.
0.25 0.75 1.25
'I
1.75
and that the up and down squarks have a common mass. The generalization to left- and right-"handed" squarks with unequal masses is explained in Dawson et al. (1984). Some restrictions on mass differences among squarks of different flavors have been deduced by Suzuki (1982). We further assume that there is no mixing between squarks, and that a quark of a given flavor and chirality couples only to the squark labeled by the same flavor and chirality. None of our general conclusions depends critically upon these assumptions. The processes leading to the production of left- and
right-handed up and down squarks in p -p collisions are
p —p —+q„qd +anything,
p —p ~(q„q„or qd qd ) +anything,
p +—p —+q *„q~+ anything,
p
+—p~(q*„q*„orq dq d)+anything,
p +p~(q*„qd or q„q—d)+ anything,
p +p~(q„q „or qdq d—)+anything,
(7.23)
(7.24)
(7.25)
(7.26)
(7.27)
(7.28)
for which the elementary cross sections are given by Eqs.
(7.13)—(7.18). Since it is nontrivial experimentally to distinguish q„jets, q'„jets, qd jets, and q d jets, we combine
all the above reactions and both chiralities for each initial state. The resulting inclusive cross section for the production of an up or down squark or antisquark with
~ y ~ & 1.5 in pp collisions is shown in Fig. 196. The larg
Ma &s (TeV/'c*)
FICx. 195. Cross sectioris for the reaction pp —+g (q„or q~ or
q *„or q d) + anything as a function of the superparticle mass,
for collider energies V s =2, 10, 20, 40, and 100 TeV, according to the parton distributions of Set 2. We have assumed equal mass for the squarks and gluino, and have included the partners of both left- and right-handed quarks. Both squark and gluino are restricted to the rapidity interval ~ y; ~ & 1.5.
Rev. Mod. Phys. , Yol. 56, No. 4, October 1984


674
C
10
10 &j. -.
II
(UdU d")2
A 0 Mev
"te~ eg &I coll~derf Phys~cs
10
10
PP (Ud D d~)2
10 1
10
—4
~2p
4p
, .&pp
1P-2
I
II I
ig
1 0-5
10—4
0,2S 0.75
I
FIG 196 C
qa
125
secti
Mass (
id, as a functi
quarks in th
pp co]1i»ons
er ener ie I- ion of the
e rapidit&ty inter~a]
utions of Set
' ' 4O an
I ark mass
2 are used.
1OO TeV Th
or co Parton dis
10-5
Acorn a'
parison of the th y interacting su
ions at 40 TeV i hiinos are
o colored
e total cms s sectio or po
s are theenn produced
est contributions ar s compone
'a e with p e t rom bo(t . ),
m sections t l
ed
(7.28), all the es i
1
ss sections ge gluino g
inc usive cross ' o
s sec
tis ""k d
un
q
evaluat d
quantit
ons 1s s
s shown for
S 1g.
dls
or pp collisions '
lar t h
qie ' othe
ase of
squark mas
g op
e l TeV/
t g.".test squark
I 1S aSSQc1e top
e lightest f qua s and th
ha
portant pr d m avors a
ol
a e, th
mecha is r
e heavy fl
m ms for
uced onl y p rt rbativel s in
ve y, processes in g
e parton distributi et 2. e c. ample even for
( d @de)2
pp
10
10 IrI. '
A 200 Mev
1p 2
10
10'
10-5 I
0.75
III
1.25
FIG. 198.
Squark Mass 8. Cross sectio
ass (TeV/c')
...d .. k 'on of up and
t1 C t nd ers are as in F'1g..
0.25
I
0.25
I)
0.75
I
~.25
FIG
Squork M
oss sec . ss (Tey a
o~n squark
ect&ons for th
c)
parton distr'b t
'squarks in — p oduction o
r s or anti
t e pair
1 96
tions of Set 2. pp co]&i»ons, ac
up and
. Cuts and
' cording t h parameters
ot e
are as in F.1g.
Rev. Mod. Ph
R . . ys. , Vol. 56, No. 4
~, o. 4, October 1984


Eichten ef al. : Supercollider physics
10 2
F h = 290 Mev 10
10
10
10
10 0.75
0.25
m Tl;
l\l
\
I I I 1.25
1.I75
10
b
10
10
10
10 I
0.25
0.I75
1.I25
1.I75
Squark Mas~ (T~Vj'c*)
FICx. 199. Cross sections for the production of a "heavy"
squark flavor in the reaction pp~tt*+ anything, according to
the parton distributions of Set 2. Cuts and parameters are as in Fig. 196.
FIG. 201. Comparison of the cross sections for gg (dotted line), gq {dotted-dashed line), and qq (dashed line) production in pp
collisions at 40 TeV, according to the parton distributions of Set 2. Also shown is the total cross section for squark or gluino
production (solid line). Cuts and parameters are as in Fig. 191.
most effectively in association with gluinos. For values of the common squark and gluino mass in excess of about 1 TeV/c, associated squark-gluino production becomes the most important reaction mechanism. As the preceding figures suggest, the importance of the squark-squark final state grows as the collider energy is reduced, for fixed superparticle masses. Raising the energy, in contrast, enhances the importance of the gluino-gluino final state. Having examined the production rates, we now turn to the more difficult question of the detection of squarks
and gluinos in the environment of a hadron collider. Any analysis of the signals for superpartners is complicated by the extreme model dependence of superparticle masses.
All that can be said with certainty is that if supersymmetry is to solve the hierarchy problem, then the lightest
superpartners of the quarks, leptons, and gauge bosons should not be much heavier than the electroweak scale, and that none of the superpartners should be heavier than
10 2
10
& = 290 Mev 10
c1
10 10
10 10
10
10 I
0.25
l
0.75 1.25
1.I75
10 1.I75 Squark Mosa (TeV/c )
FICx. 200. Cross sections for the production of a "heavy" squark flavor in pp collisions, according to the parton distribu
tions of Set 2. Cuts and parameters are as in Fig. 196.
Moss (TeVJ'c*)
FIG. 202. Comparison of the cross sections for gg (dotted line), gq (dotted-dashed line), and qq (dashed line) production in pp
collisions at 40 TeV, according to the parton distributions of Set 2. Also shown is the total cross section for squark or gluino production (solid line). Cuts and parameters are as in Fig. 191.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


676 Eichten et al. : SUpercollider physics
a few TeV/c (Fayet, 1982). In the absence of reliable theoretical guidance it is a nearly impossible task to discuss all possible decay scenarios. We shall concentrate on a few of the more plausible schemes. The strengths of couplings are prescribed by supersymmetric models. Therefore, the possible decays depend solely on the kinematic constraints imposed by the unknown mass spectrum. Possible decay schemes for the gluino are these, in increasing order of coupling strength. (i) The gluino is stable or long lived, with ~ &1-0 sec. In this case the gluino will combine with a gluon or a quark-antiquark pair to form hadrons with charges 0 and
+1. MIT bag model estimates suggest (Chanowitz and Sharpe, 1983) that these states should have masses close
to the gluino mass, if the gluino is massive. (ii) The gluino decays into a gluon and a Goldstino. The experimental signature in this case would be a gluon jet and missing transverse energy, since the Goldstino will escape undetected. (iii) The gluino is not the lightest gaugino, and decays into a quark-antiquark pair plus the lightest gaugino. In our analysis we shall assume that the lightest gaugino is the photino, as is true in many models (Fayet, 1981; Dine and Fischler, 1982; Ibanez and Ross, 1982; Nappi and Ovrut, 1982). The photino either is stable and weakly interacting (so that it escapes undetected) or decays into an undetected Goldstino and a hard photon. Thus the signature for this gluino decay mode is two jets, missing transverse momentum, and perhaps a hard photon. (iv) The gluino decays into a squark and antiquark or quark and antisquark. The signature for this mode depends on the subsequent decay of the squark [cases
(i)—(iii) below]. The dominant decay of the gluino will therefore be the last of these possibilities which is kinematically allowed. For squarks the list of possible decays is nearly identical to the gluino list (again in increasing order of coupling strength). (i) The squark is stable, so the experimental signature is a massive stable hadron (qq or q *q).
(ii) The squark decays into a quark and a Goldstino. The experimental signature in this case would be a quark jet and missing transverse momentum. (iii) The squark decays into the lightest gaugino (presumably a photino) and a quark. The resulting signature is one jet, missing transverse momentum, and possibly a hard photon. (iv) The squark decays into a quark and a gluino. The signature for this model depends on the subsequent decay
[cases (i)—(iii) above] of the gluino. The possibilities are thus one, two, or three jets and missing transverse momentum. In the three-jet case there may be an accompanying hard photon. Since the signatures for gluino and squark decays are so similar, we can discuss them both at once. Given the copious production rates we expect, the signatures of (a) a new stable hadron, (b) jets, missing transverse momentum, and a hard photon, and (c) clearly separated multijets and
missing transverse momentum are characteristic and should be relatively free of conventional backgrounds. The most pernicious of the backgrounds would seem to be heavy-quark semileptonic decays. A charged-lepton veto may thus be useful. The most difficult signature is the case in which the superpartner decays to a single jet, or coalesced multiple jets, with missing transverse momen
tum carried off by undetected particles. For such events the background associated with the semileptonic decays of heavy quarks produced in the hadronization of a standard QCD jet (in a two-jet event) may be quite severe. In the background events, energy and transverse momentum may be carried away with the undetected neutrino, while the charged lepton may be buried in a hadron jet. A pre
liminary study of the signal-to-background problem has been reported by Littenberg (1984). His Monte Carlo analysis suggests that for gluino and squark masses in ex
cess of 100 GeV/c, approximately 3000 superparticle events are required to obtain an adequate rejection of the
background by introducing a series of kinematic cuts. If it were possible to recognize leptons within jets with high efficiency, fewer events would be required to establish a squark or gluino signal. The whole area of extracting squark and gluino signatures from background can clearly benefit from much more extensive modeling.
C. Production and detection of color singlet superpartners
The fermionic partners y, Z, and W +— of the elec
troweak gauge bosons and the scalar partners e,P,7., v; of
the leptons are produced with typical electroweak strengths. As a consequence the production cross sections are considerably smaller than those for gluinos or squarks
of the same mass. The most favorable mechanism for production of y,
Z, or 8' +—is in association with a gluino or squark.
The cross sections for the elementary processes
q'~q'I'~g 'V ~
q„q~ g 8'+,
(7.29)
are given by Eqs. (7.1) and (7.2) and the coefficients listed
in Table IX. The resulting cross sections for electroweak , gaugino production in pp and pp collisions are presented
in Figs. 203—211. The rapidities of the superpartners are
restricted to ~y; ~ &1.5. For the purpose of these examples, we have taken all the gaugino masses to be equal, and have set the squark mass equal to the gaugino masses. While this is unlikely to be an accurate assumption, it should reliably indicate the discovery reach of a collider
for exploration of high masses, because the superpartner masses are likely to be similar in order of magnitude. In Figs. 205, 208, and 211, the squark mass has been fixed at
0.5 TeV/c .
We show in Figs. 203—205 the cross sections for gluino-photino associated production in pp collisions
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984


Eichten et al. : Supercollider physics 677
10
A = 290 MeV 10-1
10 10-2
10
. 10
\
\
't 00
10
-c10 ' = ~ '.
10-5
I
0.25
'~,20,40
F10
0.75 1.25 Mass (TeV/c )
1.I75
FIG. 203. Cross sections for the reaction pp.~gy+ anything
as a function of the photino mass, for collider energies Ms =2, 10, 20, 40, and 100 TeV, according to the parton distributions of Set 2. Both gluino and photino are restricted to the rapidity interval ~y; ~ &1.5. For this illustration, all squark and gaugino masses are taken to be equal.
(based on the parton distributions of Set 2), in pp col
lisions, and in pp collisions (I-=500 GeV/c ). Under the assumptions we have made here, the pp cross section
significantly exceeds the pp cross section for gaugino
masses larger than about v s /20. This corresponds to the familiar value of V ~ & 0. 1, which we have encountered in other reactions that proceed through qq interactions.
There are no significant differences between the two sets of parton distributions in this case. Similar comments ap
II II
0.75 1.25 1.75
Moss (TeVjc )
FIG. 205. Cross sections for the reaction pp —+gy + anything
as a function of the photino mass, according to the parton distributions of Set 2. Cuts and parameters are as in Fig. 203, ex
cept that M =0.5 TeV/c .
0.25
rq
gq~Z'q, gq —+ 8'q,
(7.30)
ply to the rates for gZo production (Figs. 206—208) and
for g8'++glY production (Figs. 209—211). We note
that the cross sections are substantial for a broad range of gaugino masses. We shall discuss observability below. The elementary cross sections for associated production of gauginos and squarks in the reactions
II
gf
A = 29Q MeV
gZ A = 290 Mev
10
10
C 10
10
'~
'~
II
I I I 1.75
0.75 1.25 Moss (TeV/c~) FIG. 204. Cross sections for the reaction pp —+gy+ anything
as a function of the photino mass, according to the parton distributions of Set 2. Cuts and parameters are as in Fig. 203.
a 10
10
I I '~ I I 1.I75
I
0.25 0.75 1.25 Mass (Tev/c')
FIG. 206. Cross sections for the reaction pp~gz+ anything
as a function of the zino mass, according to the parton distributions of Set 2. Cuts and parameters are as in Fig. 203.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1S84


678 Eichten et al. : Supercollider physics
10
IIII
Pp = yz
A = 290 MeV 10
i+l'-. '. 2
10
I I II
pp 9W +gW A = 29Q MeV
10
10 'L 'y ~
'
~ ~,
1i &
I I I I 1.I75
0.25 0.75 1.25 Mass (TeVj'c~)
FIG. 207. Cross sections for the reaction pp~gZ+ anything
as a function of the zino mass, according to the parton distributions of Set 2. Cuts and- parameters are as in Fig. 203.
are given by Eq. (7;9) and Table X. To arrive at the total cross sections we sum over up and down squarks and antisquarks and continue to assume that all relevant squark and gaugino masses are equal. The resulting cross sections are shown for pp~yq in Fig. 212, for pp~Z q in
Fig. 213, and for pp~W~q in Fig. 214. The cross sections in pp collisions are identical. These rates are some
what larger than those for production of an electroweak gaugino in association with a gluino. For some values of the superparticle masses, gaugino-squark production is
1
c4
10
10
0.25
I I II
0.75 1.25 Mass (TeV/c )
1.I75
the more important process because of the. additional schannel quark-exchange diagram. In view of the similarity of the cross sections and the event signatures for the gluino-gaugino and squark-gaugino final states, it will suffice to consider only one case explicitly. For our survey of decay modes and superparticle signatures we shall assume that the photino is the lightest of the superpartners. It will therefore either be stable or decay into a photon and a Goldstino. Since the photino decay will result in a hard photon plus missing transverse
FIG. 209. Cross sections for the reaction
pp~g W +—+ anything as a function of the wino mass, accord
ing to the parton distributions of Set 2. Cuts and parameters are as in Fig. 203.
10
gz
10
gl' ~
10
III
pp gW agW
A = 290 MeV
10 10
c4
O 10
10 10
I
0.25
IIII
0.75 1.25 Mass (TeV/c )
1.I75 0.25
IIII
0.75 1.25
Mass (TeVjc )
1.I75
FIG. 208. Cross sections for the reaction pp~gZ+ anything
as a function of the zino mass, according to the parton distributions of Set 2. Cuts and parameters are as in Fig. 203, except
that M =0.5 TeV/c .
FIG. 210. Cross section for the reaction
pp~g8' +—+ anything as a function of the wino mass, accord
ing to the parton distributions of Set 2. Cuts and parameters are as in Fig. 203.
Rev. Mod. Phys. , Vol. 56, No. 4, October 1984