

 4 Oct 1995

University of California - Davis UCD-95-35September 1995

PHYSICS AT A _+_\Gamma COLLIDERa

J. F. Gunion Department of Physics, University of California at Davis, Davis, CA, 95616, USA A brief overview of the physics capabalities of a _+_

\Gamma collider is given, with particular focus on special

Higgs sector opportunities.

Although design and development are at a very early stage compared to the next linear e+e\Gamma collider (NLC), and feasibility is far from proven, there is now considerable interest in the possibility of constructing a _+_\Gamma collider;1 its promise for physics was clear from the beginning.2 Two specific muon collider schemes are under consideration. A lower energy machine, the First Muon Collider (FMC), could have center-of-mass energy (ps) around 0.5 TeV with a luminosity of order 2 \Theta 1033 cm\Gamma 2 s\Gamma 1 for unpolarized beams.3 Not only would the FMC be able to accomplish everything that the NLC could (for the same luminosity), but also the FMC would be extremely valuable for discovery and precision studies of Higgs bosons produced directly in the s-channel.4 A high energy next muon collider3 (NMC) with 4 TeV c.m. energy and luminosity of order 1035 cm\Gamma 2 s\Gamma 1 would have an energy reach appropriate for pair production of supersymmetric particles and of SUSY Higgs bosons A0H0 up to very large masses, and for the study of a strongly interacting W W sector. Here, we give a brief summary of s-channel Higgs boson physics at the FMC, followed by an overview of physics at the NMC.a

1 s-Channel Higgs Physics For s-channel studies of narrow resonances, the energy resolution is crucial. The rms error oe in ps is given

by oe = (0:04 GeV) \Gamma R0:06%\Delta i ps100 GeV j where R values of 0:04 \Gamma 0:08% are most natural, with R = 0:01% achievable.5 A critical issue is how this resolution compares to the calculated total widths of Higgs bosons. For R !, 0:06%, oe can be smaller than the Higgs widths in many cases; and for R !, 0:01% the energy resolution becomes comparable to even the very narrow width of an intermediate-mass SM OE0. An s-channel Higgs resonance could be found by scanning in ps using steps of size , oe; its mass would be simultaneously determined with roughly this same accuracy in the initial scan. For sufficiently small oe, the Breit-Wigner resonance line-shape would be revealed and the Higgs width could be deduced.

However, the optimal strategy for SM Higgs (OE0) discovery at a lepton collider is to use the _+_\Gamma ! ZOE0 mode (or e+e\Gamma ! ZOE0) because no energy scan is needed. Studies of e+e\Gamma collider capabilities indicate that

a To appear in the Proceedings of the International Europhysics Conference on High Energy Physics, Brussels, 1995.

the SM Higgs can be discovered if mOE0 ! 0:7ps. If mOE0 !, 140 GeV, its mass will be determined to within6

\Delta mOE0 !, 0:4 GeV i 10 fb

\Gamma 1

L j

1 2 ; yielding, e.g., \Sigma 180 MeV

for L = 50 fb\Gamma 1.6 At the LHC the OE0 ! flfl mode is deemed viable for 80 !, mOE0 !, 150 GeV, with a better than 1% mass resolution.7 Once the OE0 signal is found, precision determination of its mass and width become the paramount goals, for which s-channel resonance production at a _+_\Gamma collider is uniquely suited.

For mOE0 ! 2mW the dominant OE0-decay channels are bb, W W ?, and ZZ?, where the star denotes a virtual weak boson. The light quark backgrounds to the bb signal can be rejected by b-tagging. For the W W ? and ZZ? channels we employ only the mixed leptonic/hadronic modes and the visible purely-leptonic ZZ? modes, taking into account the major electroweak QCD backgrounds. For all channels we assume a general signal and background identification efficiency of ffl = 50%, after selected acceptance cuts. In the case of the bb channel, this is to include the efficiency for tagging at least one b. Values of ffloeBR(X) at ps = mOE0 for X = bb, W W ? and ZZ? are presented in Fig. 1 versus mOE0 for a resolution R = 0:06%. (Here oe denotes a cross section after convolution with the Gaussian energy spectrum.) The background level (B) is essentially independent of R, while the signal rate (S) depends strongly on R.

The luminosity required to achieve noe = S=pB = 5 in the bb, W W ? and ZZ? channels is also shown in Fig. 1 -- results for R = 0:01%, 0:06% and 1% as a function of mOE0 are illustrated. For R = 0:06%, L = 1 fb\Gamma 1 would yield a detectable s-channel Higgs signal for all mOE0 values between the current LEP I limit and 2mW except in the region of the Z peak; a luminosity L , 10 fb\Gamma 1 atp

s = mOE0 is needed for 85 !, mOE0 !, 100 GeV. For R = 0:01%, noe = 5 signals are achieved with only about 1/25 of the luminosity required for R = 0:06%, implying that a search by scanning would be most efficient for the smallest possible R. If the Higgs resonance is broad, using small R is not harmful since the data from a fine scan can be rebinned to test for its presence.

Once the Higgs is observed, the highest priority will be to determine its precise mass and width. This can be accomplished by scanning across the Higgs peak. The luminosity required for this is strongly dependent upon R (i.e. oe) and the width itself. For a SM Higgs the width 1

Figure 1: The (a) OE0 signal and (b) background cross sections, ffloeBR(X), for X = bb, and useful W W ? and ZZ? final states (including a channel-isolation efficiency of ffl = 0:5) versus mOE0 for SM Higgs s-channel production with resolution R = 0:06%. Also shown: (c) the luminosity required for S=pB = 5 in the three

channels as a function of mOE0 for R = 0:01%, 0.06% and 1%.

in the intermediate mass range is generally smaller than oe; e.g. for mOE0 = 120 GeV the width is \Gamma OE0 , 0:004 GeV. A set of carefully chosen measurements is required. The minimal set is three measurements separated in ps by 2oe; the first would be taken at ps equal to the current best central value of the mass (from the initial detection scan). The second and third would be at ps values 2oe below and 2oe above the first, with about 2.5 times the integrated luminosity expended on the first. In Fig. 2 we plot the total combined luminosity required for a ffi\Gamma =\Gamma = 1=3 measurement of the width in the bb channel as a function of mOE0 . For given R, luminosity requirements vary by up to 50%, depending upon luck in placement of the first scan point, as quantified by the ratio jps \Gamma mOE0 j=oe. The excellent R = 0:01% resolution would be needed to be certain of being able to measure the total width if mOE0 , mZ. Note that the Higgs mass is also determined to the accuracy of,

ffi\Gamma .

Figure 2: The luminosity required for a ffi\Gamma =\Gamma = 1=3 measurement of the OE0 width vs. mOE0 for various choices of (jps \Gamma mOE0 j=oe; R).

In addition, the event rate in a given channel measures \Gamma (OE0 ! _+_\Gamma ) \Theta BR(OE0 ! X). Then, using the branching fractions (most probably already measured in ZOE0 associated production), the OE0 ! __ partial width can be determined, providing an important test of the Higgs coupling. For L = 50 fb\Gamma 1 and R = 0:01%, a better than \Sigma 1:5% measurement of the X = bb channel rate can be performed for all mOE0 !, 150 GeV.4 In obtaining a direct determination of \Gamma (OE0 ! _+_\Gamma ) we will be limited by the , \Sigma 7% \Gamma \Sigma 10% measurement of BR(OE0 ! bb) obtained at the NLC by combining the ZOE0 inclusive rate with the ZOE0 ! Zbb partial rate (the uncertainty in the inclusive ZOE0 measurement dominates the error).

A _+_\Gamma collider provides two particularly unique probes of the MSSM Higgs sector. First, the couplings of the h0 deviate sufficiently from exact SM Higgs couplings that it may well be distinguishable from the OE0 by measurements of \Gamma h and \Gamma (h ! _+_\Gamma ) at a _+_\Gamma collider, using the s-channel resonance process (here we use the notation h for a generic Higgs boson). For instance, in the bb channel \Gamma h and \Gamma (h ! _+_\Gamma ) \Theta BR(h ! bb) can both be measured with good accuracy. The deviations for these quantities from SM-Higgs expectations exceed 20% (10%) for mA0 !, 500 GeV (700 GeV) for all but small tan fi values.8 Unless mh , mZ , L = 50 fb\Gamma 1 of luminosity will yield a better than \Sigma 5% determination of \Gamma h, and a better than \Sigma 1% determination of \Gamma (h ! _+_\Gamma ) \Theta BR(h ! bb). However, our ability to predict BR(h ! bb) and \Gamma h is limited by uncertainty in mb, an uncertainty of order \Sigma 5% in mb leading to a \Sigma 3% (, \Sigma 10%) uncertainty in BR (\Gamma ). If we can keep systematic and statistical errors below , 10%, these quantities will probe the h0 vs. OE0 differences for mA0 values as large as 400 \Gamma 500 GeV.

The second dramatic advantage of a _+_\Gamma collider in MSSM Higgs physics is the ability to study the non-SMlike Higgs bosons, e.g. for mA0 ?, 2mZ the H0; A0. An e+e\Gamma collider can only study these states via Z? ! A0H0 production, which could easily be kinematically disallowed since GUT scenarios typically have mA0 , mH0 ?, 200-250 GeV. In s-channel production the H0; A0 can be even more easily observable than a SM-like Higgs if tan fi is not near 1. This is because the partial widths \Gamma (H0; A0 ! _+_\Gamma ) grow rapidly with increasing tan fi, implying that oeH0;A0 will become strongly enhanced relative to SM-like values. BR(H0; A0 ! bb) is also enhanced at large tan fi, implying an increasingly large rate in the bb final state. Thus, we concentrate here on the bb final states of H0; A0 although the modes H0; A0 ! tt, H0 ! h0h0; A0A0 and A0 ! Zh0 can also be useful.

Despite the enhanced bb partial widths, the suppressed (absent) coupling of the H0 (A0) to W W and ZZ means that the H0 and A0 remain relatively narrow at high mass, with widths \Gamma H0 ; \Gamma A0 , 0:1 to 3 GeV; but because mA0 , mH0 the H0 and A0 resonance peaks can overlap substantially. Since the individual resonance peaks have width comparable to or broader than the expected ps resolution for R = 0:06% and ps ?, 200 GeV, determination of the resonance peak shape would be pos2

sible by scanning in ps; the H0 and A0 widths could be extracted provided that the signal rates are sufficiently high. The results of a fine scan can be combined to get a coarse scan appropriate for broader widths.

The cross section for _+_\Gamma ! A0 ! bb production with tan fi = 2, 5 and 20 (including an approximate cut and b-tagging efficiency of 50%) is shown versus mA0 in Fig. 3 for beam resolution R = 0:01%. Overlapping events from the tail of the H0 resonance are automatically included. Also shown is the significance of the bb signal for delivered luminosity L = 0:1 fb\Gamma 1 at ps = mA0 . Discovery of the A0 and H0 will require an energy scan if Z? ! H0 + A0 is kinematically forbidden; a luminosity of 20 fb\Gamma 1 would allow a scan over 200 GeV at intervals of 1 GeV with L = 0:1 fb\Gamma 1 per point. The bb mode would yield at least a 10oe signal at ps = mA0 for tan fi ?, 2 for mA0 !, 2mt and at least a 5oe signal for tan fi ?, 5 for all mA0 !, 500 GeV. The resulting statistical significance for R = 0:06% is only noticeably worse (by a factor of 2) in the tan fi = 2 case.4 For mA0 ?, mZ (mA0 !, mZ ), the H0 (h0) has very similar couplings to those of the A0 and would also be observable in the bb mode for tan fi ?, 5. For tan fi , 2, BR(H0 ! bb) is smaller than in the case of the A0 due to the presence of the H0 ! h0h0 decay mode. For such tan fi values, detection would be easier in the h0h0 final state. Overall, discovery of both the H0 and A0 MSSM Higgs bosons (either separately or as overlapping resonances) would be possible over a large part of the mA0 ?, mZ MSSM parameter space.

Figure 3: (a) ffloeA0BR(A0 ! bb), for s-channel production of the MSSM Higgs boson A0 versus ps = mA0, for tan fi = 2, 5 and 20, beam resolution R = 0:01% and channel isolation efficiency ffl = 0:5; and (b) corresponding statistical significance of the A0 ! bb

signal for L = 0:1 fb

\Gamma 1 delivered at ps = mA

0.

The results we have quoted above do not include the spreading out of the Gaussian luminosity peak due to photon bremsstrahlung. For Higgs bosons with \Gamma h o/ oe, the cross section at ps = mh decreases proportionally to the decrease in the peak luminosity, which in turn depends upon the resolution R and ps. Roughly, for any Higgs boson with width much smaller than the energy resolution oe, a factor of !, 2 larger luminosity would be required than given in the numerical results quoted above for any

given measurement. For a Higgs boson with width much larger than oe, the increase in luminosity required for a given measurement would be much less.

Clearly, s-channel Higgs production presents exciting possibilities. The techniques discussed are generally applicable to searches for any Higgs boson or other scalar particle that couples to _+_\Gamma . If any narrow-width Higgs or scalar particle is observed at either the LHC or NLC, a _+_\Gamma collider of appropriate energy would become a priority simply on the basis of its promise as a Higgs/scalar factory.

2 SUSY An exciting possibility2 is that the NMC could be a SUSY factory, producing squark pairs, slepton pairs, chargino pairs, associated neutralinos, associated H +A Higgs, and gluinos from squark decay if kinematically allowed. If the SUSY mass scale is MSUSY , 1 TeV, many sparticles could be beyond the reach of the NLC. The LHC can produce them, but disentangling the SUSY spectrum and measuring the sparticle masses will be a real challenge at a hadron collider, due to the complex nature of the sparticle cascade decays and the presence of QCD backgrounds. The measurement of the sparticle masses is important since they are a window to GUT scale physics.

The cross sections for squarks (of one flavor in the approximation of L; R degeneracy), charginos, top and three generations of singlet quarks (from an E6 GUT model, for example) are:2 oe~uL;R = 4fi3 fb, oe ~dL;R = 1fi3 fb, oeO/\Sigma = 6fi fb oet = 8 fb, and oeQE

6 = 6fi fb, leading to 250,60, 500, 800, and 600 events, respectively, for sparticle

masses of 1 TeV, assuming ps = 4 TeV and an integrated luminosity of 100 fb\Gamma 1. The production of heavy SUSY particles will give spherical events near threshold characterized by multijets, missing energy (associated with the LSP), and leptons. There should be no problem with backgrounds from SM processes.

A supergravity model with tan fi = 5, universal scalar mass m0 = 1000 GeV and gaugino mass m1=2 = 150 GeV provides an illustration of a heavy sparticle spectrum, as follows (GeV units): ~u : 1000, ~g : 500, ~` : 1000 O/04; O/03; O/+2 : 350, O/02; O/+1 : 130, and O/01 (LSP) : 60. Consider ~u_~u production at the NMC. The dominant cascade chain for the decays is ~u_~u ! (~gu)(~g_u), followed by

~g ! O/\Sigma 1 q _q, with O/\Sigma 1 ! O/01`*; O/01q _q. The dominant branching fractions of the ~u_~u final state are

10 jets + p/T 10%

8 jets + 1` + p=T 10% 6 jets + 2` + p=T 2%

(1)

Of the two lepton events, one half will be like-sign dileptons (`+`+; `\Gamma `\Gamma ). The environment of a _+_\Gamma collider may be better suited than the LHC to the study of the many topologies of sparticle events. 3

Returning to the SUSY Higgs sector, we simply emphasize the fact that Z\Lambda ! H0A0; H+H\Gamma will allow H0; A0; H\Sigma discovery up to mH0 , mA0 , mH\Sigma values somewhat below ps=2 , 2 TeV. While GUT scenarios prefer H0; A0; H\Sigma masses above 200 to 250 GeV, such that H0A0 and H+H\Gamma pair production are beyond the kinematical reach of a 400 to 500 GeV collider, even the most extreme GUT scenarios do not yield Higgs masses beyond 2 TeV. Thus, a 4 TeV _+_\Gamma collider is guaranteed to find all the SUSY Higgs bosons.

3 Strong WLWL Scattering If a SM-like Higgs boson with m ^ O(800 GeV) does not exist, then the interactions of longitudinally polarized weak bosons WL; ZL became strong. This means that new physics must be present at the TeV energy scale. The high reach in energy of the NMC is of particular interest for study of a strongly interacting electroweak sector (SEWS) at a _+_\Gamma collider via W W fusion. The SEWS signals depend on the model for W +L W \Gamma L scattering. An estimate of the size of these signals can be obtained from the SM by taking the difference of the cross section for a heavy Higgs boson (mOE0 = 1 TeV) and that for a massless Higgs boson: \Delta oeSEWS = oe(mOE0 = 1 TeV) \Gamma oe(mOE0 = 0): The subtraction of the mOE0 = 0 result removes the contributions due to scattering of transversely polarized W -bosons. The difference \Delta oeSEWS grows rapidly with energy. At ps = 1:5 TeV (for the NLC) \Delta oeSEWS(W +W \Gamma ); \Delta oeSEWS(ZZ) = 8 fb; 6 fb, while at ps = 4 TeV (for the NMC) we find 80 fb; 50 fb, respectively. The NMC signals are nearly 10 times larger than the NLC signals.

4 Conclusions There are many other new physics possibilities for which the NMC would be a powerful probe, including

ffl extra neutral gauge bosons (the NMC could be a Z0

factory, with its decays giving Higgses and W +W \Gamma along with particle and sparticle pairs)

ffl right-handed weak bosons (the present limit on the

WR of many left-right symmetric models is MWR ?, 1:5 TeV)

ffl vector-like quarks and leptons (such as those present

in E6 models)

ffl horizontal gauge bosons X (whose presence may be

detected as an interference between t-channel X exchange and s-channel fl; Z exchanges; present limits are MX ?, 1 TeV)

ffl leptoquarks ffl compositeness

The list goes on with other exotica. The potentially very large center of mass energy and relative freedom from large backgrounds imply that muon colliders would be very exciting machines for detecting all types of new physics.

5 Acknowledgements I am grateful for the contributions of my collaborators, V. Barger, E. Berger, and T. Han. This work was supported in part by the U.S. Department of Energy.

6 References

1. Proceedings of the First Workshop on the Physics Potential and Development of _+_\Gamma Colliders, Napa, California (1992), Nucl. Instr. Meth. A350 (1994) 24;Proceedings of the Second Workshop on the Physics Potential and Development of _+_\Gamma Colliders, Sausalito, California (1994), ed. by D. Cline, to be published. 2. V. Barger et al., MADPH-95-873 Proceedings of the

Second Workshop on the Physics Potential and Development of _+_\Gamma Colliders, Sausalito, California (1994), ed. by D. Cline, to be published. 3. R.B. Palmer and A. Tollestrup, unpublished report. 4. V. Barger, M. Berger, J. Gunion and T. Han, Phys.

Rev. Lett. 75 (1995) 1462;UCD-95-27, in preparation. 5. G.P. Jackson and D. Neuffer, private communications. 6. T. Barklow and D. Burke, private communication;

P. Janot, Proceedings of the 2nd International Workshop on "Physics and Experiments with Linear e+e\Gamma Colliders", eds. F. Harris, S. Olsen, S. Pakvasa and X. Tata, Waikoloa, HI (1993), World Scientific Publishing, p. 192; and references therein. 7. ATLAS Technical Proposal, CERN/LHCC/94-43, LHCC/P2 (1994); CMS Technical Proposal, CERN/LHCC 94-38, LHCC/P1 (1994). 8. J.F. Gunion, H.E. Haber, and M. Hildreth, in preparation.

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