Experimental aspects of supersymmetry

ELSEVIER

Nuclear Physics B (Proc. Suppl.) 62A-C (1998) 89-96

PROCEEDINGS SUPPLEMENTS

Experimental Aspects of Supersymmetry Howard Baer a aDepartment of Physics, Florida State University, Tallahassee, FL 32306 In this talk, I review the present status of the event generator ISAJET for simulating weak scale supersymmetry at collider experiments. I note especially the recent ISAJET 7.29 upgrade that allows the large tanfl region of SUSY parameter space to be explored. I also discuss promising signatures for the minimal supergravity (mSUGRA) model at LEP2, the Tevatron and upgrades, the CERN LHC pp collider, and the NLC, a future e+e linear collider. In addition, I comment upon recent work on restrictions on the mSUGRA model from i.) b --* s'y decays, and ii.) the relic density of neutralinos. I finally point out how direct detection of SUSY dark matter can be very much complementary to collider searches: for large tan fl, where collider searches are most difficult, direct detection experiments are most promising.

1. I n t r o d u c t i o n Supersymmetry[1] is a topic which has fascinated many theorists, and by now it is included as a standard feature in m a n y model builders recipe book. In spite of its beauty, and the many theoretical problems it solves, experimentally, it has yet to be verified. A crucial question is: if sup e r s y m m e t r y exists, how will we know? This is a very model dependent question. Even if supers y m m e t r y (SUSY) exists, can it somehow be verified experimentally? If SUSY exists but is broken at some high mass scale rn >> (_9(1) TeV, we may never know about its existence. However, there seem to be some solid reasons to expect it to be intimately related to the weak scale in particle physics. Foremost among these is that its existence at around the TeV scale stabilizes quantum corrections to the Higgs scalar bosons. The Higgs boson(s) seem necessary to give mass to the intermediate vector bosons in realistic models. In addition, the heavy top quark mass is just what is needed in SUSY models to radiatively break electroweak symmetry. There is even the well-known experimental hint of TeV sparticles, the existence of which allows for gauge coupling unification at grand unified mass scales ~ 1016 GeV. If we conjecture that SUSY particles exist at the TeV scale, then they ought at least to be accessible to near future collider searches. The 0920-5632/98/$19.00 © 1998 Elsevier Science B.V. All fights reserved. PII S0920-5632(97)00646-4

next question is: how would TeV SUSY manifest itself? There are m a n y possibilities for models, but mainly they break up into two classes. Both classes assume SUSY is broken in a hidden sector of the model. However, one class assumes that gravity acts as the messenger for SUSY breaking[2], while the other class assumes SUSY breaking is communicated by gauge interactions[3]. In this talk I will focus on the experimental ramifications of gravity-mediated SUSY breaking models. Partly, this is because they seem prettier and more economical than their counterparts. For more details on the phenomenology of gauge mediated SUSY breaking models, see for instance Ref. [41. For gravity mediated models, it is assumed that gravitational interactions give rise to universal TeV scale soft SUSY breaking terms at some high scale m ~ 1016 - 1019 GeV, where the former number might be preferred by the previously mentioned gauge coupling unification. Q u a n t u m corrections and threshold effects may well badly invalidate the universality assumption. Really, one needs to examine the experimental ramifications of as many models as is possible, and hope that SUSY is recognizable at experimental facilities. In practise, such scrutinization of models is laborious and painstaking if done in detail. So as a first step, we examine models with universal soft SUSY breaking terms, and hope nature turns

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out to be something close to this. In the gravity mediated models, usually the gravitino acquires a weak scale mass and is extremely weakly interacting, thus decoupling from much of phenomenology. Then, the lightest neutralino usually comes out to be the lightest SUSY particle (LSP), and it is absolutely stable in R-parity conserving models, thus making a good candidate for cold dark matter. Implications of LSP dark matter will be addressed at the end of this talk. To sum up, a well motivated SUSY model is often called the minimal supergravity model (mSUGRA), where it is assumed all scalars get the same mass m0 at MGUT, while all gauginos acquire a common mass m l / 2 , and all trilinear soft terms unify to A0. The mSUGRA model breaks down to the Minimal Supersymmetric Standard Model (MSSM) below MCUT, so that sparticle masses can be calculated by renormalization group evolution from MCUT to Mweak. Requiring radiative electroweak symmetry breaking yields a predictive model based only on the parameters m0, ml/2, Ao, tan/3 and sgn(#),

(1)

where tan/3 is the ratio of Higgs field vevs and Iz is the superpotential Higgs mass term, whose magnitude is specified by requiring radiative electroweak symmetry breaking. Once a model is specified, then the experimental consequences, at least for collider experiments, can be examined via the use of event generator programs. Several of us have been involved with incorporating the necessary SUSY particle production cross sections and decay rates into the event generator ISAJET[5] the past several years, so that SUSY models can be directly connected to collider detector simulations. In that way, we better learn how SUSY might manifest itself, and also exactly what sort of detector needs to be built so that SUSY won't escape experimental scrutinization. I S A J E T allows the input of either the above mSUGRA parameter set, or else a more general MSSM one. Previously, ISAJET was only valid for tan/3 < 10. Recently, ISAJET was upgraded to allow reliable event generation in the large tan/3 regime as well[6]; this regime is favored by models including t, b and 7- Yukawa

coupling unification.

2. SUSY at Large tan/3 When tan/3 becomes large (tan fl > 10) the b-quark and r-lepton Yukawa couplings are no longer negligible, and their effects must be accounted for both in the calculation of sparticle masses, and also in the calculation of sparticle production and especially decay rates. Incorporation of b and r Yukawa couplings in particle spectra calculations is relatively straightforward. First, one must account for mixing of the left and right stau and sbottom gauge eigenstates. One must also be careful to include staus and sbottoms appropriately in the minimization of the scalar potential, which determines among other things the Higgs boson masses. We found that at large tan/3 the pseudoscalar Higgs mass was unstable for variations in scale choice chosen for minimization of the RGE improved l-loop effective potential, for scale choices Q ... Mz. Empirically stable values of mA were generated if we chose a much higher scale choice Q ~ ~ . The latter scale choice was also preferred by calculations which actually searched for an optimized scale choice. As an example, various SUSY particle masses are shown in Fig. 1 versus variation in tan/3. We see that the "rl and bl masses d e c r e ~ e significantly with tan/3, until decays such as Z2 ~ ~lr and W1 --* "~lv can take place. Also, the mass m A decreases markedly from it value at small tan/3; this can lead to among other things, enhanced Higgs boson production at colliders and also improved prespects for the direct detection of SUSY dark matter. We have also included in ISAJET version 7.29 new calculations for the decay rates of ~,Wi,2i,~,~,~,b~,~,h,H,A and H + decays, including Yukawa couplin~ and mixing effects. In particular, the W~ and Z~ full three body decays had never before been calculated, so these results are new. The ~ --* ttZi and ~ --* tbW~ calculations had been previously calculated by Bartl et. al.[7]; our results were checked to agree with theirs. Some sample branching fractions are shown in Fig. 2. In the first two frames, it is clear that

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Run 2 sometime in 1999, operating at yrs -~ 2 TeV and collecting ,-, 2 fb -1 of data. The CERN LHC collider expects to turn on around 2005 and amass ,~ 10 - 100 fb -1 of integrated luminosity in the early portion of their runs. There is hope to build as well an e+e - linear collider a n d / o r a muon collider to operate around v ~ -,~ 300 - 500 GeV, though as yet there are no firm construction plans. Let's review what each machine can hope to do with respect to the m S U G R A model.

Figure 1. Sparticle masses versus tan13. '

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3.1. S U S Y at L E P 2 There are several promising avenues to be explored by LEP2 experiments with regards to mSUGRA. Perhaps the most likely scenario would be for LEP2 experiments to discover a light Higgs scalar h, which is possible over much of parameter space for small tan/~. If t a n ~ is large, then the h mass becomes generally too heavy to be accessible to LEP2. In Ref. [8], we evaluated SUSY signals against SM backgrounds, and found regions where a 5a signal could be seen assuming 0.5 fb -1 of integrated luminosity. The reach of LEP2 at ~ = 190 GeV is plotted in Fig. 3 in the m o vs. m l / 2 plane for tan/3 -- 2 and # < 0. The TH region is excluded by theoretical constraints, while the EX region is excluded by previous searches at LEP1. We see in Fig. 3 that LEP2

might discover the chargino via e+e - ~ W1W1 if m l / 2 < 100 GeV. If m l / 2 is larger, but m0 is small, then selectron pairs might be accessible to LEP2 SUSY searches. Finally, there is an intermediate region where e+e - ---* Z 1 Z 2 is accessible via the dilepton signal. These reaches change somewhat for other choices of SUSY parameters.

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The LEP2 e+e - collider has recently begun operation at C E R N at v ~ ,-, 180 GeV. Experiments soon hope to collect on the order of 100 pb -1 of data. The Fermilab Tevatron expects to begin

3.2. S U S Y at t h e T e v a t r o n At the Fermilab Tevatron, for current luminosity samples, the best reach is still typically due to t h e / ~ T + j e t s signal which is due to gluino and squark production followed by cascade decays. This should change during Run 2. The higher luminosity should allow significant regions of parameter space to be e x p i r e d via the clean trilepton signM from pp --* W1 Z2 -* 3g, which has very low backgrounds. This signal is mainly visible for lower values of tan/3. The reach is plotted

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Figure 3. Regions of mSUGRA parameter space accessible to LEP190. 250 "'1

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in Fig. 4[9]. The bricked areas are excluded by theory, while hatched areas are excluded mainly by LEP2 constraints. The black boxes are points accessible to current Tevatron data samples. The grey boxes indicate points accessible to Tevatron Run 2, mainly via 3~ searches. The white boxes indicate additional parameter space accessible to TeV33 experiments collecting 25 fb -1 of integrated luminosity. The reach plots integrate over a variety of search channels, although the clean 3l channel is best for high luminosity. More detailed results are presented in Ref. [9]. We note that the x'ed points are where no SUSY signal is accessible to any Tevatron upgrade considered, so that Tevatron experiments can probe some interesting regions of parameter space, but can't by any means do a definitive search for mSUGRA. 3.3. S U S Y at t h e L H C The SUSY reach of the LHC was evaluated in Ref. [10], and the regions of accessible parameter space are plotted in Fig. 5 assuming a modest 10 fb -1 of integrated luminosity. The ~ region is where direct slepton p r o d u c t ~ n should be visible, while the region marked Wx Z2 is where clean 3£ signals should be visible. The upper contours denote the reach of LHC for SUSY in a variety of

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search channels. The best of these is the singleisolated lepton plus jets +/~T channel: here, m~ ,,~ 2 TeV can be probed with only modest luminosity! It is evident that LHC should be able to make a complete search for mSUGRA. This comclusion is true even if the LSP decays hadronically via R-violating decay, assuming the gauge and Yukawa interactions still dominate sparticle production and decay processes[Ill. Recently, much work was done[12] to see how LHC could do on precision SUSY mass measurements. A key to solv~g the SUSY spectrum puzzle could be found if Z2 --* ~£Z1 with a large rate. Then rn(£g) < m.~2 - m-51 offers hope of further disentangling the sparticle masses[13]. 3.4. S U S Y a t t h e N L C The reach of a possible NLC e+e - collider operating at v ~ -- 500 GeV was worked out in Ref. [14], and is shown in Fig. 6, along with the reach of LHC, TeV33 and other NLC energy options. The NLC would of course probe the entire mSUGRA parameter space via Higgs searches. The sparticle search regions are significant, but more limited than LHC. The real strength of an NLC is that if sparticles are discovered, then precision, model independent mea-

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Figure 5. Regions of mSUGRA parameter space accessible to LHC searches -.,

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surements of masses and other parameters are possible[15]. If SUSY exists, then an NLC type machine will be essential for doing sparticle spectroscopy. 4. b --* s3' C o n s t r a i n t s o n S U S Y

Aside from direct production of SUSY particles at colliders, SUSY can also be searched for indirectly, for instance, in flavor changing b decays, such as b -~ sT. Numerous papers have been written giving the b -+ s7 branching fraction as a function of various model parameter spaces. Data from CLEO[16] constrain the b --* s7 branching ratio to be between 1-4.2x 10 -4 at 95% CL. Model calculations in leading-log QCD could be compared with data, but the large uncertainty due to QCD corrections hampered somewhat the effort to get meaningful comparisons of data with theory. Recently, much work has been done[17] towards achieving a next-to-leading order calculation of b --* s% We have incorporated recent QCD improvements to the b --* s7 decay rate with the mSUGRA model predictions[18]. These improvements include: 1.) inclusion of multiple scales in the RGE running of the Wilson coefficients, 2.)

inclusion of NLO anomalous dimension matrix elements for the Wilson coefficient running, and 3.) inclusion of virtual and bremsstrahlung effects in the decay rate calculation at scale Q ,-~ mb. With these improvements, the uncertainty in model predictions due to QCD scale choice drops from 25% to 9%. We show results of some branching fractions in mSUGRA parameter space in Fig. 7, where each contour must be multiplied by 10 -4 . In this frame, we see a rate larger than that allowed by CLEO in the lower-left corner, thus giving an important restriction on model parameter space. For the opposite sign of tt (# > 0), this restriction vanishes. For larger values of tan/3 ~ 10, most of parameter space for # < 0 (# > O) is excluded (allowed). 5. N e u t r a l i n o D a r k M a t t e r

Another important restriction on SUSY models comes from cosmology. If the LSP is indeed stable, then they should have been produced in the early universe, and should comprise much of the dark matter today. It is straightforward but lengthy to calculate the relic density of neutralinos in the mSUGRA model. To do so, one must solve the Boltzmann equation which governs the neutralino number density in an expanding uni-

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Figure 7. Branching fractions for b --* sT (x 104).

Figure 8. Contours of neutralino relic density in the mEUGRA model.

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6. D i r e c t D e t e c t i o n o f t h e L i g h t e s t N e u tralino If at any given moment we have tremendous numbers of neutralinos floating through our bodies, it is reasonable to try to detect some of them. Such dark matter detectors have been built, and newer, more sensitive versions are coming on-line in the near future. The idea is to try to detect the very weak neutralino-nucleus collision. To do so will require detectors functioning near absolute zero to remove thermal background. Recent calculations[20] have been performed for a 73Ge

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verse. This procedure requires evaluation of the thermally averaged neutralino pair annihilation cross section. We have performed such a calculation[19], including all relevant annihilation diagrams, relativistic thermal averaging, and threshold effects, with careful integration over BreitWigner poles. Sample results are shown in Fig. 8. For ~ h 2 > 1, the universe would be younger than 10 billion years old, so these regions are excluded. Parameter space points with 0.15 < ~ h 2 < 0.4 are favored by cosmological models with mixed dark matter, e.g. part neutrinos and part neutralinos.

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detector, for mSUGRA parameter space. For low tan/3 detection rates are usually very low, especially for # < 0. However, as tan/3 increases, detection rates increase as well. This is due in part to scattering though virtual Higgs bosons. At large tan/3, the Higgs couplings are enhanced and the heavy Higgs boson mass decreases. Some sample detection rates for tan/3 = 35 are shown in Fig. 9. Detectors are aiming at achieving a detection rate of --~ 10 -2 events/kg/day by the year 2000. One can see from the figures that in this case, direct detection of neutralinos may well be possible in the low m l / 2 region of parameter space, which is most favored by fine tuning constraints. It is interesting that the large tan/3 region of parameter space is where direct detection of SUSY dark matter is most promising; this region is exactly the same region where collider searches for SUSY are expected to be most difficult. 7. C o n c l u s i o n s In conclusion, I believe the next ten years will be very exciting times for particle physics. Evidence for supersymmetry may well be found in rare decays, or by table-top cryogenic detectors. Direct production and detection of supersymmet-

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Figure 9. Contours ofevents/kg/dayin 73Ge dark matter detector 1000 //

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tic particles could occur at one or several of the many collider experiments. The LHC can seemingly make a thorough search for weak scale supersymmetry, thereby verifying or excluding the weak scale SUSY hypothesis. Either way, such knowledge will help point the way to a more fundamental understanding of the structure of the universe. REFERENCES

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For recent reviews, see H. Baer et. al., hepph/9503479, to appear in Electroweak Breaking and Physics Beyond the Standard Model, T. Barklow et. al., Editors (World Scientific, to appear); Snowmass 96 Supersymmetry Working Group Report, J. Bagger et. al., hep-ph/9612359 and sub-group reports cited therein.

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