Searching for NLSP Sbottom at the LHC
aa r X i v : . [ h e p - ph ] A p r Searching for NLSP Sbottom at the LHC
M. Adeel Ajaib a , Tong Li b , and Qaisar Shafi c Bartol Research Institute, Department of Physics and Astronomy,University of Delaware, Newark, DE 19716, USA (Dated: June 27, 2018)We study the collider phenomenology of sbottom-bino co-annihilation scenario atboth the 7 TeV and 14 TeV LHC. This co-annihilation scenario requires that theNLSP sbottom and LSP bino masses are apart by no more than about 20% or so,and for M ˜ b > M b + M ˜ χ , the sbottom decays exclusively into b + ˜ χ . We proposea search for sbottom pairs through b ¯ b plus missing energy. By scanning the massparameters M ˜ b and M ˜ χ , we investigate the discovery limits of sbottom and bino inthe M ˜ b − M ˜ χ plane with at least 5 σ significance at the LHC, for varying integratedluminosities. It is shown that with at least 5 fb − luminosity, the 7 TeV LHC canexplore a narrow region satisfying the 20% co-annihilation condition. For the 14 TeVLHC with 10 (100) fb − luminosity, the discovery limit of M ˜ b is 360 (570) GeV. a email: [email protected] b email: [email protected], communication author c email: shafi@bartol.udel.edu I. INTRODUCTION
Low scale supersymmetry, augmented by an unbroken Z matter (R-) parity, largelyovercomes the gauge hierarchy problem encountered in the Standard Model (SM) and alsoprovides a compelling cold dark matter candidate. In the mSUGRA/constrained minimalsupersymmetric model (CMSSM) [1] , as well as in many other realistic models, the lightestneutralino (LSP) is stable [2] with a relic density that is compatible with the WMAP darkmatter measurements [3]. To be compatible with the latter, and assuming thermal relicabundance, a pure Higgsino or wino LSP mass should be around a TeV or so [4], which isabout an order of magnitude larger than the most sensitive discovery region ( ∼
100 GeV) ofthe ongoing direct detection experiments. On the other hand, the small annihilation crosssection of a pure bino LSP with mass of around 100 GeV does not permit one to easilyreproduce the required relic dark matter abundance [4].A variety of scenarios that enhance the bino annihilation cross section have been proposed.For instance, the LSP could be a suitable bino-Higgsino admixture with mass ∼
100 GeVand compatible WMAP relic density [5] (and references therein). A somewhat differentand well studied option is co-annihilation, which is realized in the CMSSM as bino-stauor bino-stop co-annihilation [6, 7]. In this case the bino and the relevant NLSP (whereNLSP stands for next to lightest supersymmetric particle) sfermion are sufficiently closetogether in mass, such that the ensuing co-annihilation processes in the early universe allowone to reproduce the desired bino relic density. Another interesting scenario of this kind isbino-gluino co-annihilation. This scenario is not possible in the CMSSM, but it has beenimplemented in models with non-universal gaugino masses [8], and a class of (third family)Yukawa unified models [9]. The collider signatures of these three (stop, stau, gluino) co-annihilation scenarios have been discussed in the literature [10–12] and references therein.A somewhat less well studied region of the MSSM parameter space is the so-called sbot-tom co-annihilation (or NLSP sbottom) scenario. This was proposed in the context ofsupersymmetric SU (5) with b − τ unification and non-universal supersymmetry breakingscalar mass terms for the ¯5 and matter multiplets [13]. More recently, the NLSP sbot-tom scenario was re-considered in Ref. [14], motivated by studies related to the InternationalLinear Collider (ILC). Yet another suggestion, put forward in Ref. [15], is to employ non-universal gaugino masses. Be that as it may, in our study we do not specify any particulartheoretical models to explore the sbottom-bino co-annihilation scenario.A satisfactory implementation of the NLSP sbottom scenario with the correct WMAPcompatible LSP relic density requires a relatively small mass difference, less than or of order20%, between the sbottom and the bino [13–15]. The sbottom decay into b -jet, ˜ b → b ˜ χ ,then becomes the unique channel if the mass difference is larger than b quark mass andsuggests a search for NLSP sbottom via pp → ˜ b ˜ b ∗ X → b ¯ b + (cid:0)(cid:0) E T . (1)This search was performed with the first Run II data in the D0 experiment, but at thattime the b -tagging techniques were not available. Other groups have studied the detectionpossibility at the Tevatron [16] and ILC [14] but, to the best of our knowledge, the analysisfor LHC is still lacking. The di- b jet events is also the leading search channel for the SM-likeHiggs boson, but the identification criteria is different.This paper is organized as follows. In section II we study, without relying on any specificNLSP sbottom model, the collider phenomenology of this scenario. We discuss here thesignal properties and the relevant backgrounds. The NLSP sbottom discovery limits at the7 and 14 TeV LHC are discussed in section III, and our conclusions are summarized insection IV. II. SBOTTOM CO-ANNIHILATION AND NLSP SBOTTOM SEARCH AT THELHC
With the requirement that M ˜ b − M ˜ χ M ˜ χ < ∼ , (2)the NLSP sbottom essentially decays into a bottom quark and LSP ˜ χ , and consequentlythe relevant kinematic constraint is M ˜ b > M b + M ˜ χ (3)if this two-body decay is allowed. Together with the requirement of sbottom-bino co-annihilation, we have the following M ˜ χ region for a given sbottom mass: M ˜ b / . < M ˜ χ < M ˜ b − M b . (4) -4 -3 -2 -1
200 400 600 800 1000pp → b ~ b ~ M b1 (GeV) s ( pb ) FIG. 1. The total cross section of sbottom pair production at the 7 TeV (dashed) and 14 TeV(solid) LHC. The renormalization and factorization scales are taken to be the sbottom mass.
We discuss below the discovery potential of NLSP sbottom and LSP ˜ χ at the LHC withthe mass boundary in Eq. (4).The current bound on the sbottom mass comes from LEP II, namely M ˜ b >
90 GeV [17].The pair production rate of sbottom with O (100) GeV mass is around the pico-barn level.For NLSP sbottom, we focus on the sbottom pair production followed by the unique two-body decay ˜ b → b ˜ χ . Namely, pp → ˜ b ˜ b ∗ X → b ¯ b + (cid:0)(cid:0) E T , (5)induced by gluon fusion and q ¯ q annihilation processes. In principle, there also exist same signsbottom pair productions ˜ b ˜ b and ˜ b ∗ ˜ b ∗ . They arise from third generation parton scatteringwith t -channel neutralino exchange. Due to the smallness of the parton distribution functions(PDFs) of third generation sea quarks at large pp collision energy, we ignore this contributionin our study. Therefore, the sbottom production and subsequent decay only depend on thetwo mass parameters M ˜ b and M ˜ χ . In Fig. 1 we show the total cross section of sbottompair production at the 7 TeV (dashed) and 14 TeV (solid) LHC.The decays, on average, of the relatively long lived B -mesons in the final states takeplace O (mm) away from the primary interaction vertex. With the detection at the so-called secondary vertex, tagging jets with decaying B -mesons significantly reduces the QCDjet background. The b -jet production in the SM is mainly due to gluon splitting, and sothe b -jets always arise as pairs. We therefore propose to tag two b -jets both in the signaland background events, and the SM b ¯ b production would become the leading irreduciblebackground. Besides the b quark, the dark matter particles ˜ χ also appear in sbottomdecays. The missing transverse energy (cid:0)(cid:0) E T is another characteristic feature of the signal.The irreducible SM background for (cid:0)(cid:0) E T is from Z production, with the branching fractionof Z invisible decay ( Z → ν ¯ ν ) of 20%. The other source of b -jet production in the SM isfrom top quark decay originating from top pair production. It can mimic our signal if both W ’s decay leptonically and the charged leptons are not detected, which is assumed to occurif the leptons are too soft with transverse momentum p ℓT <
10 GeV and are not in centralrange with pseudo-rapidity | η ℓ | > .
5. There also exist reducible backgrounds due to otherjets being mis-identified as b -jets. The SM backgrounds we consider in our study are then b ¯ b ; b ¯ bZ, jjZ with BR ( Z → ν ¯ ν ) = 20% ; t ¯ t → b ¯ bℓ + ℓ − ν ¯ ν with undetected leptons . (6)We generate the SM background events with Madgraph/Madevent [18] and pass them intoPythia [19] for parton shower and hadronization. Due to the uncertainty of mis-measurementin jet energy or momentum in the detector, the b ¯ b events without Z can also induce miss-ing energy. The Pythia output is then fed into the fast detector simulation PGS-4 [20], inorder to simulate the important detector effects. The b -tagging efficiency and mis-taggingrate in PGS-4 are based on the Technical Design Reports of ATLAS and CMS, and we usethe default values in our analysis. The following basic kinematical cuts on the transversemomentum ( p T ), the pseudo-rapidity ( η ), and the separation in the azimuthal angle-pseudorapidity plane (∆ R = p (∆ φ ) + (∆ η ) ) between two jets have been employed for jet selec-tion [21]: p jT >
15 GeV , | η j | < . , ∆ R jj > . . (7)For the SUSY signal we also use Pythia to generate events and then forward to PGS-4to smear the observed particles as well. The hardness of the b -jet in final states dependson the mass difference ∆ M = M ˜ b − M ˜ χ . The larger the ∆ M we impose, the harder the b -jet is, as also the missing transverse energy (cid:0)(cid:0) E T , in which case more events would pass theselection cuts. The (cid:0)(cid:0) E T is reconstructed according to the smeared b -jets. In Fig. 2 we showthe (cid:0)(cid:0) E T distribution of the signal and backgrounds including basic cuts in Eq. (7), and b -jet σ (pb) @ 7 TeV ˜ b ˜ b ∗ b ¯ b b ¯ bZ ( → ν ¯ ν ) jjZ ( → ν ¯ ν ) t ¯ t basic cuts+2 b tagging 0.22 7716 0.108 0.049 0.05 (cid:0)(cid:0) E T >
40 GeV 0.15 8 0.07 0.033 0.029 S T > . , ∆ φ ( (cid:0)(cid:0) E T , b ) > . b ˜ b ∗ signal and SM backgrounds after different cuts at 7 TeVLHC. The masses of ˜ b and ˜ χ are assumed to be 200 GeV and 150 GeV respectively. and mis- b jet tagging efficiency from PGS. One can see that the (cid:0)(cid:0) E T of backgrounds is rathersoft because the dominant background source is pure b ¯ b , and its missing energy is just fromsmall uncertainty of b -jets mis-measurement. We find that by requiring a significant (cid:0)(cid:0) E T cut,namely (cid:0)(cid:0) E T >
40 GeV for 7 TeV , (cid:0)(cid:0) E T >
50 GeV for 14 TeV , (8)the SM backgrounds can be significantly suppressed. However, b ¯ b is still the leading back-ground and one order of magnitude larger than our signal because of its extremely largesize to begin with. To further suppress the contribution from processes where the missingenergy comes from jet energy mis-measurement, we require that (cid:0)(cid:0) E T is not parallel to any b -jets in events [16], namely ∆ φ ( (cid:0)(cid:0) E T , b ) > . . (9)Furthermore, the b ¯ b events are expected to be back-to-back, and thus peaked at smalltransverse sphericity S T ∼
0, as shown in Fig. 3. Around S T ∼ .
2, the behavior ofbackgrounds reaches a level two orders of magnitude lower than the peak value. We thusrequire [22] S T > . b ¯ b events. After these selection cuts, the SM b ¯ b background can be completelyeliminated. The remaining leading backgrounds are b ¯ bZ with invisible Z decay and t ¯ t withundetected charged leptons. The efficiencies of different cuts for the signal ˜ b ˜ b ∗ and SMbackgrounds at 7 TeV and 14 TeV LHC are collected in Tables I and II respectively. (GeV) missT E - E ve n t s / G e V / f b -1 (GeV) missT E - E ve n t s / G e V / f b
14 TeVsignalbackgroundssignalbackgrounds
FIG. 2. ˜ b ˜ b ∗ signal and SM background events vs. transverse missing energy (cid:0)(cid:0) E T at 7 TeV (left)and 14 TeV (right) LHC with 1 fb − luminosity. The masses of ˜ b and ˜ χ are assumed to be 200GeV and 150 GeV respectively. T S - E ve n t s / . / f b -1 T S - E ve n t s / . / f b
14 TeVsignalbackgroundssignalbackgrounds
FIG. 3. ˜ b ˜ b ∗ signal and SM background events vs. transverse sphericity S T at the 7 TeV (left) and14 TeV (right) LHC with 1 fb − luminosity. The masses of ˜ b and ˜ χ are assumed to be 200 GeVand 150 GeV respectively. III. RESULTS FOR NLSP SBOTTOM DISCOVERY LIMIT
As mentioned earlier, we are interested in the mass parameter region constrained byEq. (4). Thus, we scan the relevant mass parameters of ˜ b and ˜ χ in that region. The signalsignificance is obtained in terms of Gaussian statistics, given by the ratio S/ √ B of signaland background events with different integrated luminosities. In Figs. 4 and 5 we show σ (pb) @ 14 TeV ˜ b ˜ b ∗ b ¯ b b ¯ bZ ( → ν ¯ ν ) jjZ ( → ν ¯ ν ) t ¯ t basic cuts+2 b tagging 0.942 20151 0.276 0.13 0.206 (cid:0)(cid:0) E T >
50 GeV 0.51 12 0.137 0.052 0.112 S T > . , ∆ φ ( (cid:0)(cid:0) E T , b ) > . b ˜ b ∗ signal and SM backgrounds after different cuts at 14 TeVLHC. The masses of ˜ b and ˜ χ are assumed to be 200 GeV and 150 GeV respectively. the discovery region of the NLSP sbottom with > σ significance in the M ˜ b − M ˜ χ planeat 7 TeV LHC for integrated luminosities 1 fb − , 2 fb − and 5 fb − , and 14 TeV LHC forintegrated luminosities 10 fb − and 100 fb − , respectively. The straight lines correspond tothe kinematic limit relation from the decay ˜ b → b ˜ χ , and the sbottom-bino co-annihilationrequirement ∆ M < M ˜ χ . The middle region between the straight lines is what wescanned. Generally, when the parameter space extends to the kinematic limit, the discoverysensitivity vanishes because the b -jets become too soft and thus cannot survive the p jT and (cid:0)(cid:0) E T cuts. One can see that only with at least 5 fb − luminosity the 7 TeV LHC can explorethe mass region 190 GeV < ∼ M ˜ b < ∼
265 GeV satisfying the 20% co-annihilation boundary,and a very narrow range above the 20% co-annihilation boundary line (with width < ∼ − , 2 fb − and 5 fb − can probe NLSP sbottom masses of 215 GeV, 260 GeV, and 300 GeVrespectively. For 14 TeV LHC the discovery region corresponding to 20% co-annihilationboundary is much broader. The relevant discovery limit is M ˜ b ∼
360 GeV (570 GeV) for10 fb − (100 fb − ) luminosity.Finally, let us note that the heavy gluino pair production channel may provide an inter-esting avenue to search for NLSP sbottom at the LHC. As an example, consider a low-energyspectrum which has, say, M ˜ g ∼ . M ˜ b ∼
200 GeV. The total production crosssection for pp → ˜ g ˜ gX → bb ˜ b ∗ ˜ b ∗ + · · · is about 7 fb at the 14 TeV LHC, with approximately27% branching ratio of gluino decay into b + ˜ b ∗ . The b -jet and NLSP sbottom will be highlyboosted, and the signal from heavy gluino decays will consequently be two extremely hardjets with one of them being the collimated sbottom. However, if we require the two ener-getic b -jets to be identified, the production rate will be further suppressed because the b -jettagging efficiency declines as its p T increases, with p T ∼ M ˜ g / ∼
600 GeV in this case. It - - - M b 1 = M b + M Χ c o - a n n . H % L c o - a n n . H % L
100 200 300 400 500100200300400500 M b1 H GeV L M Χ H G e V L FIG. 4. Discovery region of the NLSP sbottom with > σ significance at 7 TeV LHC in the M ˜ b − M ˜ χ plane for integrated luminosities of 1 fb − , 2 fb − and 5 fb − . The curves for thekinematic limit of ˜ b → b + ˜ χ decay channel and NLSP sbottom co-annihilation requirement arealso displayed.
14 TeV100 fb -
10 fb - M b 1 = M b + M Χ c o - a n n . H % L c o - a n n . H % L
200 400 600 800 10002004006008001000 M b1 H GeV L M Χ H G e V L FIG. 5. Discovery region of the NLSP sbottom with > σ significance at 14 TeV LHC in the M ˜ b − M ˜ χ plane for integrated luminosities of 10 fb − and 100 fb − . The curves for the kinematic limitof ˜ b → b + ˜ χ decay channel and NLSP sbottom co-annihilation requirement are also displayed. is also difficult to tag the b -jet in the decay products of the boosted sbottom. Therefore,the NLSP sbottom search from gluino production will require a more careful analysis of the b -jet structure and we leave it for future study.0 IV. CONCLUSION
We have explored the collider phenomenology of sbottom-bino co-annihilation scenarioat the LHC. The NLSP sbottom is assumed to be slightly more massive than the LSPbino, namely M ˜ b − M ˜ χ < ∼ M ˜ χ , with M ˜ b > M b + M ˜ χ , such that ˜ b decays into b + ˜ χ with 100% branching fraction. We present a search for sbottom pairs through b ¯ b plusmissing energy final states. By scanning the mass parameters M ˜ b and M ˜ χ , we investigatethe discovery limits of sbottom and bino at the 7 TeV and 14 TeV LHC with differentintegrated luminosities. It is shown that the 7 TeV LHC can probe only a narrow regionsatisfying the 20% co-annihilation boundary with at least 5 fb − luminosity. For 14 TeVLHC the discovery limit is M ˜ b ∼
360 GeV and M ˜ b ∼
570 GeV for luminosity of 10 fb − and100 fb − respectively. We also briefly explored the possibility of detecting NLSP sbottomfrom heavy gluino decay. Acknowledgment
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