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Discovering Supersymmetry with Like-sign Dileptons

Supersymmetry may be discovered at hadron colliders by searching for events similar to the top quark signal of two isolated leptons. In the case of gluino production, the most distinguishing feature is that in half the events the two leading leptons have the same sign. We demonstrate the remarkable sensitivity of this gluino signature at both the Fermilab Tevatron Collider and at the Superconducting Super Collider. Techniques for approximately determining the gluino mass are discussed.


Introduction
A hallmark in the search for supersymmetry would be the discovery of the gluino or the squarks, the supersymmetric partners of the gluon and the quarks [1] .
Many previous discussions of supersymmetry phenomenology at hadron colliders have centered on the "classic" signature for gluino or squark production: clusters of hadrons ("jets") and large missing transverse energy with no associated hard leptons. The missing-energy signature arises from events in which gluinos and/or squarks are produced and subsequently decay into jets and the lightest supersymmetric particle (LSP). The LSP, like the neutrino, will escape collider detectors.
In this Letter, we focus on the striking experimental signature of two isolated leptons which can arise from gluino pair production. Half of the events of this type will have leptons with the same sign of electric charge. This signature, which is analogous to the opposite-sign lepton signal for the top quark, may yield sensitivity much superior to the missing-energy gluino signature at the Fermilab Tevatron Collider or at the Superconducting Super Collider (SSC), depending on the parameters of the supersymmetric model. Moreover, the same-sign lepton signature can also be utilized to provide an estimate of the gluino mass. A preliminary version of the results contained here appeared in Refs. 2-3. Complementary work that also considered the like-sign dilepton signature can be found in Refs. 4-7.

Gluino Decays and the Dilepton Signature
In this Letter, we examine gluino searches at hadron colliders in the context of the minimal supersymmetric extension of the Standard Model (MSSM). We concentrate on g g production under the assumption that M g < M q (otherwise, g → q q would be the dominant gluino decay mode, and the phenomenology of squarks would be our primary concern). Gluino signatures depend in detail on the gluino branching ratios into neutralino and chargino ⋆ final states [8−10] . The masses and couplings of the neutralinos and charginos [11] are determined by the MSSM parameters µ, tan β and the gaugino mass parameters, M 1 and M 2 . Furthermore, under a unification assumption for the gaugino mass parameters, it follows that: In gluino pair production, the most prominent missing-energy signature arises from g → qq χ 0 1 decays, when χ 0 1 , the lightest neutralino, is assumed to be the LSP. However, substantial suppression of the g → qq χ 0 1 decays is found; e.g. for M g = 180 GeV, B( g → qq χ 0 1 ) < 0.4 (and possibly much smaller, depending upon µ and tan β). The suppression is even more dramatic for heavier gluinos (M g > ∼ 500 GeV), where B( g → qq χ 0 1 ) is no greater than 0.14 [9,10] . The dominant gluino decays are those into chargino and heavier neutralino states which in turn decay into lighter neutralinos and/or charginos. Although in a cascade decay chain the LSP is ultimately emitted and escapes detection, the missing-energy signature is significantly degraded as compared to gluino decays in which the LSP is emitted in the initial decay. Fortunately, the leptons frequently produced in typical decay chains provide a viable signal for g g production.
Over a large range of supersymmetric parameter space, the dominant gluino decay mode is g → qq χ ± 1 , where χ ± 1 is the lightest chargino. [9] Leptons can result from decays such as χ ± 1 → W ± χ 0 1 → ℓ ± ν χ 0 1 , where the W ± is either on-shell (if ⋆ The neutralinos and charginos are mixtures of the supersymmetric partners of the γ, Z, and H 0 bosons and of the W ± and H ± bosons respectively. kinematics allow) or off-shell. If the sleptons are lighter than the chargino, then the two-body decays χ ± 1 → ℓ ± ν → ℓ ± ν χ 0 1 and χ ± 1 → νℓ ± → ℓ ± ν χ 0 1 are allowed and may dominate. † Since the gluino is a Majorana fermion, ‡ it has the distinctive property of decaying with equal probability into fermions and antifermions. Thus, an excellent signature for pair production of gluinos results from events in which both gluinos decay to a chargino of the same sign, yielding like-sign dileptons (ℓ + ℓ + or ℓ − ℓ − ) in the final state. The probability for the production of like-sign and opposite-sign leptons is equal, and the characteristics of the two classes of final states are identical. Observation of this distinctive result would be extremely helpful in identifying the origin of the events. It should also be noted that the likesign dilepton signature remains viable in models with explicit R-parity breaking in which the LSP decays and does not produce a missing-energy signature. [12] Of course, like-sign dilepton events can arise in events involving primary squark production. If M q < M g , dilepton signatures from q q events could contain both like-sign and opposite-sign components, depending on the relative squark decay branching ratios to produce final state neutralinos and charginos. (If t → t χ 0 1 decays occur, the additional isolated leptons from t decay would need to be included in the analysis.) Since the parameters of the squark and the g/ χ + / χ 0 sectors are independent, the specific squark branching fractions are model dependent. As a result, we focus in this paper on the case of M q > M g . It then follows that B( q → q g) ∼ 100% so that q q and q g production yield g g events with two or one extra quark jet, respectively. But, the direct g g cross section is by far the largest † In many models of supersymmetry the ℓ and ν are significantly lighter than the squarks. Thus, such decays are not incompatible with the heavy squark assumption of this paper. ‡ Here, we use a broader definition of Majorana to include neutral particles that transform under real representations of the underlying Standard Model gauge group. and yields the dominant contribution to the like-sign dilepton signal.
In the numerical work in this paper, we have taken the the branching ratio for gluino decay to the lightest chargino to be B( g → qq ′ χ ± 1 ) = 0.58, a result which holds to good accuracy for all |µ| > ∼ M g /3, m Z . [9] Moreover, this value for the branching ratio is approximately valid for nearly all MSSM parameters of relevance to the Tevatron gluino search. ⋆ If the ℓ and ν are heavier than the chargino, the chargino decays dominantly into the LSP plus a real (or virtual) W ± [13] , which then decays 22% of the time into electrons and muons. Thus the branching ratio for the decay chain g → qqℓ ± ν χ 0 1 is likely to be as large as 13%, with equal probability to produce a lepton of either sign. (For simplicity, the τ -lepton will be neglected from , and M χ ± 1 < m W + M χ 0 1 , then the two-body decays of the χ ± 1 to ℓν and/or νℓ will have ∼ 100% branching ratio into leptonic final states (including the τ -lepton). If we neglect τ -leptons, we find B( g → qqℓ ± ν χ 0 1 ) close to 40%. A remarkable 15% of all g g events would yield a dilepton final state.
Given the large cross-sections for gluino pair production at the Tevatron Collider and the SSC [14] , there would exist a potentially large and interesting sample of events. These events would have hadronic jets (two from each gluino), missing energy due to the LSP and neutrinos in the final state, and a dilepton pair which can come in one of the following like-sign combinations: e ± e ± , e ± µ ± , µ ± µ ± , and the corresponding opposite-sign combinations. The events would be very similar ⋆ For example, when M g < ∼ 200 GeV and tan β > ∼ 4, B( g → qq ′ χ ± 1 ) varies between about 45% and 65% as µ is varied.
to those arising from tt production in which the leptons come from primary decays of the t and t. Thus, distinguishing the source of opposite-sign events might be difficult. Because the efficiency for tagging b-jets is low and because some fraction of g g events will contain b-jets from a hard radiated gluon, b-jets may not be a useful tool for separating tt from g g events. For this reason we will focus on likesign dilepton final states for which tt production yields a background only through t → bℓ − ν and t → bX, b → cℓ − ν (or the corresponding charge-conjugated decay chain). This background would be quite small since the lepton from the b decay would very rarely be isolated.

Gluino Search at the Tevatron and SSC
We have evaluated the rates for the dilepton signal in gluino pair production at both the Tevatron and SSC energies. In order to roughly account for realistic experimental conditions, we have employed a parton-level Monte Carlo, which included resolution smearing but no fragmentation, to model the g g events † We also examined the impact of the higher-order process g gg on our results. [16] In examining the latter process, we have placed a transverse momentum cut on the extra g such that the g gg cross section is approximately the same as the g g cross section. A more precise treatment would incorporate a full one-loop analysis, but is unlikely to affect our basic conclusions. We find that the only impact of the extra radiated gluon is upon the size of the cross section even when cuts are imposed.
The shapes of the distributions we have examined (described below) are essentially unaltered at both Tevatron and SSC energies. † A description of a similar program to analyze the characteristics of supersymmetric events at the CERN pp collider can be found in ref. 15. We first present our analysis for Tevatron energies. The surprisingly large potential for gluino discovery at the Tevatron becomes apparent by giving the number of dilepton (opposite-plus like-sign) events obtained in a 25 pb −1 year.
To estimate the rates for detectable dilepton events at the Tevatron, we assume a trigger which requires that the leading (secondary) lepton has E T > 15 (10) GeV. In addition, we require |η| < 2.5 and isolation for both leptons. ‡ Associated hadronic jets are not required. The probability that events pass these cuts depends in detail upon the masses of the particles involved in the decay chains, but is roughly 50% for much of parameter space. We have explored a range of supersymmetric parameters for which the mass M χ ± 1 varies between about 45 GeV (its current lower bound from LEP data [17] ) and 80 GeV, while letting the gluino mass vary between 100 GeV (the present experimental lower bound [18] ) and 200 GeV. In the corresponding range of MSSM parameter space, the mass of the LSP ( χ 0 1 ) is approximately given by M g /6.
For χ ± 1 → W ± * χ 0 1 , the 1.6% net branching ratio quoted earlier yields between 70 and 1 dilepton events (of which half are like-sign) per 25 pb −1 at the Tevatron for M g between 100 and 160 GeV. In contrast, if the χ ± 1 decays to ℓν and/or ℓ ν, the larger 15% net branching ratio can result in up to 1100 (15) dilepton events for M g = 100 (200) GeV, depending on the decay mode and the various masses. ‡ In this paper, we define an isolated lepton to be one that is separated by at least 0.3 units in ∆R ≡ [(∆η) 2 + (∆φ) 2 ] 1/2 from any parton (or "merged parton jet" if two or more partons are within 0.7 units in ∆R of each other). are expected from tt production for m t = 140 GeV, but all of these have oppositesign leptons. Thus, for comparable gluino and top quark masses, the additional requirement of two isolated like-sign leptons would reduce the top quark rate to a level far below that from gluinos. However, a top quark significantly lighter than the gluino might require that additional cuts be made to separate the two signals.
The event rate depends strongly on the lepton cuts. The lepton spectrum itself is quite sensitive to decay modes and decay product masses. For the chargino threebody decay to χ 0 1 ℓν via a virtual W , the lepton spectrum depends primarily on . Because of the current experimental limit of M ℓ > 44 GeV [17] , most leptons from ℓ decay pass our cuts for the M χ 0 1 values employed. Thus, even for the relatively large gluino masses of 160 and 180 GeV, the ℓν decay event rates illustrated are large enough to be in possible conflict with observed rates at the Tevatron. In contrast, as illustrated in Table 1, the event rate associated with χ ± 1 → ℓ ν decays could be very small since small values of M χ ± 1 − M ν are possible, leading to a soft lepton that is unlikely to pass our cuts. However, even for M g = 180 GeV, if the ν mass is not close to M χ ± 1 then the event rate for the ℓ ν mode is large.
Thus, if very few or no like-sign dilepton events are found after accumulating L = 25 pb −1 , then improved limits on the gluino mass (as a function of other MSSM parameters) will be attainable. If χ ± 1 → W ± * χ 0 1 is the dominant decay, a modest improvement of M g > 120 GeV is possible, based on the like-sign dilepton search. In contrast, if ℓ ν or ℓν decays of the χ ± 1 are dominant and the ℓ spectra are not suppressed by a small mass difference, then limits of order M g > ∼ 200 GeV will be obtained over the large region of parameter space for which B( g → qq χ ± 1 ) is substantial.
Assuming that one has succeeded in isolating gluino candidates, it is important to ask if one can estimate the mass of the gluino, and the masses of the decay products. We have performed detailed studies and find that the most useful distributions (at the Tevatron) for this purpose are E ℓ max T , the E T of the most energetic lepton and E j max T , the transverse energy of the jet with largest E T . ⋆ For any given decay chain, these can be used to estimate the mass differences, and the overall event rate can then be used to determine the absolute mass scale, provided statistics are adequate. Scenarios consistent with current Tevatron rates would require L > 100 pb −1 to achieve a ±25 GeV uncertainty in the measurement of M g . Further details will be given elsewhere.  The value of the variable M est can be illustrated using W -mediated decays of the χ ± 1 in the limit of |µ| ≫ M 1 , M 2 where M χ 0 1 ∼ M g /6 and M χ ± 1 ∼ M g /3. [13] In Fig. 1 we give the M est distribution shapes that would be obtained after one SSC year for M g = 300 and 350 GeV. The distributions contain 4500 and 4000 events, respectively. We see that M est provides a clear separation between the two gluino mass cases considered. We estimate that a gluino mass determination accurate to within 25 GeV should be possible in the mass range considered here.
In contrast, the E ℓ max T and E j max T histograms (not shown) provide a much weaker gluino mass determination, barely allowing one to distinguish M g = 350 GeV from M g = 300 GeV. However, using the M est distribution, we estimate that the gluino mass can be determined to better than 10% if the gluino decay product masses are known. This determination can be cross-checked with theoretical expectations for the total event rate.

Conclusions
The like-sign signature for g g production provides a powerful tool, both for discovering evidence for supersymmetry and for estimating the gluino mass. It is the Majorana nature of the gluino that yields this striking signature. At the Tevatron collider, under the most favorable assumptions concerning gluino cascade decay branching fractions, gluino production could yield as many as 1100 dilepton events (after significant lepton cuts) in the current 25 pb −1 run, of which half would be like-sign. Since large numbers of events are not seen, many new constraints on the masses of the g, χ ± 1 , χ 0 1 , ℓ and ν will be obtained. If the handful of dilepton events currently observed at the Tevatron were due to g g production, an integrated luminosity of at least L = 100 pb −1 would be required to obtain a ±15% estimate of the gluino mass. At the SSC, very large like-sign dilepton event rates are predicted, and a gluino mass determination would be possible for masses up to 2 TeV or more.
For M g < 1 TeV, the gluino mass determination would be accurate to about 15% (or even better if the gluino decay product masses are known). For a very heavy gluino, like-sign dilepton events provide the cleanest discovery signature.