Less is More when Gluinos Mediate
Compressed mass spectra are generally more difficult to identify than spectra with large splittings. In particular, gluino pair production with four high energy top or bottom quarks leaves a striking signature in a detector. However, if any of the mass splittings are compressed, the power of traditional techniques may deteriorate. Searches for direct stop/sbottom pair production can fill in the gaps. As a demonstration, we show that for and , limits on the stop mass at 8 TeV can be extended by least 300 GeV for a 1.1 TeV gluino using a search. At 13 TeV, the effective cross section for the gluino mediated process is twice the direct stop pair production cross section, suggesting that direct stop searches could be sensitive to discover new physics earlier than expected.
Less is More when Gluinos Mediate
SLAC, Stanford University
With the recent discovery of the Higgs boson with a mass of 125 GeV by the ATLAS  and CMS  collaborations at the LHC, the issue of naturalness is brought into focus. If the solution to the hierarchy problem is that the Standard Model is a subset of a supersymmetric (SUSY) theory, then naturalness suggests that the mass of the supersymmetric counterpart to the top quark, the stop (), is near the electroweak scale GeV. For various reasons such as gauge unification or the 2-loop radiative corrections to the Higgs boson mass, one may also expect a light supersymmetric counterpart of the gluon, the gluino (), with mass TeV. The spectrum can remain natural even if all other colored super partners have masses well into the TeV range or beyond. In -parity conserving SUSY theories, gluinos would be pair produced; the gluino pair production cross section is much larger than the cross section for direct pair produced stops. For example, at 8 TeV, the cross section for pair produced stops with mass 800 GeV is about 0.002 pb whereas the cross section for stops produced from the decay of 1 TeV pair produced gluinos is about 0.02 pb . Both ATLAS [4, 5, 6, 7, 8] and CMS [9, 10, 11, 12, 13, 14] have searched extensively for the scenario of gluino mediated stop production at the LHC and have excluded natural spectra with large mass splittings that have gluinos with mass below about 1.5 TeV.
When the mass splitting between the stop and the lightest neutralino is very small, many of the traditional techniques for identifying gluino pair production are ineffective. Recognizing the phenomenological similarity between when and the direct production of when , depicted in Fig. 1, suggests that searches for the later can be recast as searches for gluinos. Appendices A.1 and A.2 systematically describes the various compressed scenarios possible in gluino-mediated stop/sbottom production, but the remainder of this paper focuses on the gluino mediated compressed stop scenario.
2 Limits on Compressed Gluino Mediated Stop Production
The lost sensitivity to compressed from direct gluino searches with multi-top quark, multi- quark, or multi-lepton final states can be recovered by direct stop searches. As shown schematically in Fig. 1, the final state for the gluino mediated compressed stop is the same as the direct stop production. There are only subtle differences due to the fact that the gluino is a fermionic color octet, instead of a scalar triplet like the stop, so there will be small differences in angular distributions and radiation patterns between jets. However, most analysis techniques are not sensitive to these effects. One non-negligible difference is the electric charge, as stops can have the same charge when from gluinos, but must be oppositely charged for direct stop production. For this reason, gluino searches with multi-top//lepton final states loose sensitivity to the gluino mediated compressed stop scenario, but same-sign lepton searches can retain sensitivity. However, we will soon see that one- and zero-lepton searches will be more powerful, due to the much larger branching ratio. Both ATLAS [15, 16, 17, 18, 19, 20, 21, 22] and CMS [23, 24, 25, 26, 27, 28] have searched for direct stop pair production using a variety of techniques to target the rich phenomenology possible in stop decays. The current limits on direct stop production for a massless neutralino reach about GeV in both the one lepton and zero lepton final states. In the next section, we will discuss how to recast these limits for gluino pair production.
2.1 Reinterpreting Direct Stop Limits
For a massless neutralino, one can translate the limits on111To ease the notation, we will drop the subscripts on the stop and the neutralino - the smallest mass eigenstates are assumed throughout. into limits on with by solving the equation , from e.g. the numbers published by Ref. . The superscript is used to distinguish the mass hierarchy in the direct stop production (no subscript) from the mass hierarchy in the gluino mediated stop production in the reinterpretation. To extend the limits toward , one needs to choose stop masses such that the top quark and neutralino from the gluino decay at should be comparable to the top quark and neutralino from the stop decay at . Define the two-body phase space momentum:
where GeV is the top quark mass . Then, given a pair excluded by a direct stop search, and from , the re-interpreted excluded stop mass is given by the solution to . The solution is quartic in , so in general there can be up to four real solutions. Fortunately, two solutions are negative (or imaginary) and of the two possible positive solutions, only one can be smaller than and thus there is at most one physical solution. The translation for the high mass stops given in the recent 8 TeV ATLAS stop search222Similar limits exist for the ATLAS all-hadronic search  and both the CMS leptonic  and hadronic searches . in the one lepton final state  are shown in Table 1.
The above procedure will produce limits for the gluino mediated compressed stop so long as . However, this is an artificial constraint - exclusion power increases in the top/neutralino momentum , which is increasing for decreasing . Therefore, it is a safe assumption that if the point is excluded, then the point will also be excluded. One can take this argument one step further. If the maximum stop mass excluded by direct searches is , then it is artificial for the maximum excluded gluino mass to be , because the acceptance increases with gluino mass. One can extend the limits to larger gluino masses by noting that the acceptance for a particular model to pass all signal region requirements depends only on and not on or directly and then extrapolating to higher values of beyond . Figure 3 shows the acceptance from the ATLAS stop search in the one lepton final state  as a function of . The observation that the acceptance only depends on is confirmed by the fact that there is one curve independent of the stop mass. For large values of , the acceptance should be roughly linear in as the missing momentum in the event is linear in . Therefore, we fit the curve beyond to a straight line for extrapolating the acceptance to higher values of . Values of can be declared excluded if , where is the excluded beyond the Standard Model number of events from the published search (5.3 events).
One can do even better than naively recasting limits based on by tightening thresholds on the key variables , , , , etc. [30, 18, 31, 32], but studying this change would require a careful assessment of the change in the background yield which is beyond the scope of this paper. Limits can additionally be improved by combining multiple channel (one lepton and zero lepton).
2.2 Derived Limits
The re-casted direct stop limits are shown Fig. 3 alongside existing limits from the ATLAS same-sign search  and the inclusive one lepton333A similar search exists in the zero lepton final state, with slightly weaker limits  search . The same-sign limits are optimistic because the selection in Ref.  requires a third hard jet, which is not part of the leading order description of the final state. Estimates based on calculations with MadGraph5_aMC@NLO version 18.104.22.168  indicate that the fraction of the time an additional jet from initial or final state radiation has enough to pass the jet selection is roughly 40%. This agrees well with the three jet selection efficiency published in auxiliary material Table 64  of the ATLAS search for a model with large top mass for which kinematically the soft -quark jets will not pass the hard jet threshold. As the mass splitting between the stop and the neturalino goes to zero, the reduction in the limit for the highest mass splitting reduces by GeV (not shown). The inclusive one lepton search is based on generic variables such as , , effective mass, etc. and is not optimized for the final state (the limits may even degrade as ). The improvement over these existing analyses for the reinterpreted direct search are shown in shaded blue in Fig. 3. The darkest blue is from the strict re-interpretation based on the strategy leading up to Table 1. The light blue area below the dark blue area is assumed excluded because the signal efficiency increases for the larger mass splitting. The light blue area to the right of the dashed line is from interpolating and extrapolating the efficiency and comparing to the published limit on allowed beyond the Standard Model events. For a 1.1 TeV gluino, the inclusive one lepton limit is extended vertically by about 300 GeV.
3 Conclusions and Future Outlook
Natural, weak scale SUSY is a compelling paradigm for models of new physics. The sensitivity to such models with a nearly mass degenerate stop and neutralino can be extended by repurposing searches for direct stop pair production. The major implications of this work are:
Even though the decay products of a stop (or a sbottom) might be missed due to detector thresholds, the other gluino decay product(s) can empower complementary search techniques targeting one step decay chains with fewer objects in the final state. Direct searches could do even better with targeted optimization to higher final states. No limits currently exist (that the author knows of) for the gluino mediated compressed sbottom.
At 13 TeV, searches for direct stop/sbottom pair production might be able to discover SUSY much earlier than expected because the direct stop/sbottom cross section is much smaller than the gluino cross section. Table 2 summarizes the relative increase in cross sections. Larger masses generally have a larger increase in cross section from 8 to 13 TeV center of mass energy. Thus, since the sensitivity to gluino masses at 8 TeV is much higher than the stop masses, the increase from 8 to 13 TeV is bigger for the gluinos. At the edge of the 8 TeV sensitivity, the expected increase in the yield of gluinos is twice the corresponding yield for stops.
The discovery of SUSY could be within reach of the Run II of the LHC. All possibilities for natural SUSY should be targeted, including those with compressed scenarios. If there is a light enough gluino to mediate, more territory for light stops and sbottoms will be accessible to the direct searches with the early data.
|13 TeV/8 TeV||13 TeV/8 TeV|
We would like to thank Till Eifert and Michael Peskin for useful discussions and Tommaso Lari for referring us to the limits in Ref. . BN is supported by the NSF Graduate Research Fellowship under Grant No. DGE-4747 and by the Stanford Graduate Fellowship.
A Compressed Scenarios
When or , gluinos can decay via an on- or off-shell stop to a final state. Since each top quark decays to a quark and an on-shell boson, the final state results in four high -quarks and large missing energy from the neutralinos () with the possibility of many leptons from the decays, some pairs of which can have the same charge. A natural SUSY spectrum would also suggest that the SUSY partner of the left-handed bottom quark, the sbottom (), should also be light and if produced via can give rise to four -quarks and up to four leptons as well if . There are not many Standard Model processes that produce many high energy -quarks, multi- or same-sign leptons in association with large missing energy and so such techniques are very powerful.
However, the high energy, high multiplicity final states from gluino pair production may become difficult to identify experimentally for compressed mass spectra. In this section, we systematically consider such scenarios by enumerating all mass hierarchies. Throughout, (or ) and (or ). Stops and sbottoms have both flavor conserving and flavor changing decays. The flavor preserving decays are discussed in Sec. A.1 and those with flavor changing decays are discussed in Sec. A.2.
a.1 Flavor Preserving Decays
First, suppose that or . The possible hierarchies are depicted schematically in Fig. A.1. The large mass splittings in Fig. A.1a are well covered by traditional gluino searches that look for e.g. multi- final states with large missing momentum. The highly compressed spectrum in Fig. A.1d is not possible to identify without additional initial or final state radiation that would lead to a mono-jet topology, which is beyond the scope of this analysis. For the , the scenario shown in Fig. A.1b cannot be too compressed because the top quark would have to be very off-shell for its decay products to be too soft to detect. As falls below , the top and stop resonances will go off-shell and compete in order to conserve energy. Since , the stop width is unsuppressed. When the off-shell top mass is below the mass, the price for taking the top further off-shell is more than for the stop and so it is likely that the scenario for stop production in Fig. A.1b is still well-covered by existing searches. In contrast, for , the scenario shown in Fig. A.1b can be compressed all the way to in which case the -quark from the direct gluino decay might be too soft to measure experimentally. This is phenomenologically similar to the models in Fig. A.1c. The scenarios shown in Fig. A.1c are a clear source of compressed gluino decays for which traditional searches may loose sensitivity and are well-motivated by stop-neutralino co-annihilation to produce the correct DM cosmological abundance [38, 39, 40]. When the stop (or sbottom) and neutralino are nearly mass degenerate, the phenomenology of the is basically the same as (or replace and ), and are covered by the analyses discussed in the main body of the paper.
a.2 Flavor Changing Decays
The flavor changing decays are and . Figures A.2 and A.3 schematically show the possible mass hierarchies for the stop and sbottom decays, respectively. Many of the hierarchies are well-covered by traditional searches. These include the scenarios in Figures A.2a,b,c and A.3a,c,e. Other scenarios are already covered by the compressed models discussed in the body of the text, including Figures A.2d and A.3g. The equivalent (direct sbottom searches) equivalent of the models (direct stop searches) discussed in the text include Figures A.2g and A.3d. Two signatures which are not covered by direct stop/sbottom searches and are possibly uncovered by direct gluino searches include the and (possibly without much ) signatures in Figures A.2e,f and A.3b. Dedicated study of such models, and the sensitivity of existing searches, is beyond the scope of this paper but should be part of the LHC search program in Run II and beyond.
-  ATLAS Collaboration. Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett., B716:1–29, 2012.
-  CMS Collaboration. Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett., B716:30–61, 2012.
-  Michael Kramer et al. Supersymmetry production cross sections in collisions at TeV. 2012.
-  ATLAS Collaboration. Search for new phenomena in final states with large jet multiplicities and missing transverse momentum at TeV proton-proton collisions using the ATLAS experiment. JHEP, 1310:130, 2013.
-  ATLAS Collaboration. Search for strong production of supersymmetric particles in final states with missing transverse momentum and at least three -jets at = 8 TeV proton-proton collisions with the ATLAS detector. JHEP, 1410:24, 2014.
-  ATLAS Collaboration. Search for supersymmetry at TeV in final states with jets and two same-sign leptons or three leptons with the ATLAS detector. JHEP, 1406:035, 2014.
-  Georges Aad et al. Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using TeV proton–proton collision data. JHEP, 1409:176, 2014.
-  Georges Aad et al. Search for squarks and gluinos in events with isolated leptons, jets and missing transverse momentum at TeV with the ATLAS detector. JHEP, 1504:116, 2015.
-  CMS Collaboration. Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at = 8 TeV. JHEP, 1406:055, 2014.
-  CMS Collaboration. Search for supersymmetry in pp collisions at TeV in events with a single lepton, large jet multiplicity, and multiple b jets. Phys. Lett., B733:328–353, 2014.
-  CMS Collaboration. Search for new physics in events with same-sign dileptons and jets in pp collisions at = 8 TeV. JHEP, 1401:163, 2014.
-  CMS Collaboration. Exclusion limits on gluino and top-squark pair production in natural SUSY scenarios with inclusive razor and exclusive single-lepton searches at 8 TeV. Technical Report CMS-PAS-SUS-14-011, CERN, Geneva, 2014.
-  CMS Collaboration. Search for supersymmetry in pp collisions at sqrt(s) = 8 Tev in events with two opposite sign leptons, large number of jets, b-tagged jets, and large missing transverse energy. Technical Report CMS-PAS-SUS-13-016, CERN, Geneva, 2013.
-  CMS Collaboration. Search for supersymmetry in pp collisions at sqrt(s) = 8 TeV in events with three leptons and at least one b-tagged jet. Technical Report CMS-PAS-SUS-13-008, CERN, Geneva, 2013.
-  ATLAS Collaboration. Search for a supersymmetric partner to the top quark in final states with jets and missing transverse momentum at TeV with the ATLAS detector. Phys. Rev. Lett., 109:211802, 2012.
-  ATLAS Collaboration. Search for direct top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in TeV collisions using 4.7 of ATLAS data. Phys. Rev. Lett., 109:211803, 2012.
-  ATLAS Collaboration. Search for a heavy top-quark partner in final states with two leptons with the ATLAS detector at the LHC. JHEP, 1211:094, 2012.
-  ATLAS Collaboration. Search for top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in 8 TeV collisions with the ATLAS detector. JHEP, 1411:118, 2014.
-  ATLAS Collaboration. Search for direct pair production of the top squark in all-hadronic final states in proton-proton collisions at TeV with the ATLAS detector. JHEP, 1409:015, 2014.
-  ATLAS Collaboration. Search for direct top-squark pair production in final states with two leptons in pp collisions at TeV with the ATLAS detector. JHEP, 1406:124, 2014.
-  ATLAS Collaboration. Measurement of Spin Correlation in Top-Antitop Quark Events and Search for Top Squark Pair Production in pp Collisions at TeV Using the ATLAS Detector. Phys. Rev. Lett., 114(14):142001, 2015.
-  ATLAS Collaboration. Search for pair-produced third-generation squarks decaying via charm quarks or in compressed supersymmetric scenarios in collisions at TeV with the ATLAS detector. Phys. Rev., D90(5):052008, 2014.
-  CMS Collaboration. Search for top-squark pair production in the single-lepton final state in pp collisions at = 8 TeV. Eur. Phys. J., C73(12):2677, 2013.
-  CMS Collaboration. Searches for third generation squark production in fully hadronic final states in proton-proton collisions at sqrt(s)=8 TeV. 2015.
-  CMS Collaboration. Search for top squarks decaying to a charm quark and a neutralino in events with a jet and missing transverse momentum. Technical Report CMS-PAS-SUS-13-009, CERN, Geneva, 2014.
-  CMS Collaboration. Search for top-squark pairs decaying into Higgs or Z bosons in pp collisions at TeV. Phys. Lett., B736:371–397, 2014.
-  CMS Collaboration. Search for supersymmetry with razor variables in collisions at TeV. Phys. Rev., D90(11):112001, 2014.
-  CMS Collaboration. Inclusive search for supersymmetry using the razor variables in collisions at TeV. Phys. Rev. Lett., 111(8):081802, 2013.
-  K.A. Olive et al. Review of Particle Physics. Chin. Phys., C38:090001, 2014.
-  Yang Bai, Hsin-Chia Cheng, Jason Gallicchio, and Jiayin Gu. Stop the Top Background of the Stop Search. JHEP, 1207:110, 2012.
-  Michael L. Graesser and Jessie Shelton. Hunting Mixed Top Squark Decays. Phys. Rev. Lett., 111(12):121802, 2013.
-  Benjamin Nachman and Christopher G. Lester. Significance Variables. Phys. Rev., D88(7):075013, 2013.
-  ATLAS Collaboration. Susy-2013-15 auxillary material, 2014.
-  J. Alwall et al. The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. JHEP, 1407:079, 2014.
-  ATLAS Collaboration. Susy-2013-09 auxillary material, 2014.
-  Alexander L. Read. Presentation of search results: The CL(s) technique. J. Phys., G28:2693–2704, 2002.
-  Christoph Borschensky et al. Squark and gluino production cross sections in pp collisions at 13, 14, 33 and 100 TeV. Eur. Phys. J., C74(12):3174, 2014.
-  Andrea De Simone, Gian Francesco Giudice, and Alessandro Strumia. Benchmarks for Dark Matter Searches at the LHC. JHEP, 1406:081, 2014.
-  Antonio Delgado et al. The light stop window. Eur. Phys. J., C73(3):2370, 2013.
-  Stefano Profumo and Carlos E. Yaguna. A Statistical analysis of supersymmetric dark matter in the MSSM after WMAP. Phys. Rev., D70:095004, 2004.