Natural SUSY Endures
DDESY 11-193CERN-PH-TH/265
Natural SUSY Endures
Michele Papucci,
1, 2
Joshua T. Ruderman,
1, 2 and Andreas Weiler
3, 4 Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Department of Physics, University of California, Berkeley, CA 94720 DESY, Notkestrasse 85, D-22607 Hamburg, Germany CERN TH-PH Division, Meyrin, Switzerland
Abstract
The first 1 fb − of LHC searches have set impressive limits on new colored particles decayingto missing energy. We address the implication of these searches for naturalness in supersymmetry(SUSY). General bottom-up considerations of natural electroweak symmetry breaking show thathiggsinos, stops, and the gluino should not be too far above the weak scale. The rest of the spectrum,including the squarks of the first two generations, can be heavier and beyond the current LHC reach.We have used collider simulations to determine the limits that all of the 1 fb − searches pose onhiggsinos, stops, and the gluino. We find that stops and the left-handed sbottom are starting tobe constrained and must be heavier than about 200-300 GeV when decaying to higgsinos. Thegluino must be heavier than about 600-800 GeV when it decays to stops and sbottoms. Whilethese findings point toward scenarios with a lighter third generation split from the other squarks,we do find that moderately-tuned regions remain, where the gluino is just above 1 TeV and all thesquarks are degenerate and light. Among all the searches, jets plus missing energy and same-signdileptons often provide the most powerful probes of natural SUSY. Overall, our results indicatethat natural SUSY has survived the first 1 fb − of data. The LHC is now on the brink of exploringthe most interesting region of SUSY parameter space. a r X i v : . [ h e p - ph ] O c t ontents I. Introduction II. SUSY Naturalness Primer III. Current status of SUSY searches IV. The Limits
V. Implications for SUSY Models VI. Conclusions Acknowledgments A. Validation of the analyses implementations B. Brief description of “ATOM” C. Projections for the current analyses References . INTRODUCTION
The experiments of the Large Hadron Collider (LHC) at CERN are now searching ex-tensively for signals of supersymmetry (SUSY). So far, the experiments have announced nodefinitive sign of new physics. Instead, they have used the first 1 fb − of data to performan impressive number of searches that have produced increasingly strong limits on coloredsuperparticles decaying to missing energy [1–23]. These limits have led some to conclude,perhaps prematurely, that SUSY is “ruled out” below 1 TeV. We would like to revisit thisstatement and understand whether or not SUSY remains a compelling paradigm for newphysics at the weak scale. If SUSY is indeed still interesting, it is natural to ask: what arethe best channels to search for it from now on? After all, the first fb − at 7 TeV were the“early days” for the LHC, with many superparticles still out of reach.We believe that naturalness provides a useful criterion to address the status of SUSY.Supersymmetry at the electroweak scale is motivated by solving the gauge hierarchy prob-lem and natural electroweak symmetry breaking is the leading motivation for why we mightexpect to discover superpartners at the LHC. The naturalness requirement is elegantly sum-marized by the following tree-level relation in the Minimal Supersymmetric Standard Model(MSSM), − m Z | µ | + m H u . (1)If the superpartners are too heavy, the contributions to the right-hand side must be tunedagainst each other to achieve electroweak symmetry breaking at the observed energy scale .Eq. 1 also provides guidance towards understanding which superparticles are required tobe light, i.e. , it defines the minimal spectrum for “Natural SUSY”. As we review in detail inSect. II, the masses of the superpartners with the closest ties to the Higgs must not be toofar above the weak scale. In particular, the higgsinos should not be too heavy because theirmass is controlled by µ . The stop and gluino masses, correcting m H u at one and two-looporder, respectively, also cannot be too heavy. The masses of the rest of the superpartners,including the squarks of the first two generations, are not important for naturalness and can We note that equation 1 applies to the tree-level MSSM at moderate to large tan β , but, as we will discussbelow, similar relations hold more generally.
3e much heavier than the present LHC reach.Naturalness in SUSY [24–30] has been under siege for quite some time. The LEP-2 limiton the Higgs mass, m h > . Little Hierarchy Problem : in order to raise the Higgs mass above the LEP-2 limitwith radiative corrections, large stop masses are required, m ˜ t > ∼ − m H u in equation 1, leading to fine-tuning.2. Direct LHC Limits : the stops and gluino masses are directly constrained, leadingto fine-tuning in equation 1.These two fine-tuning problems are intrinsically different, the first being an indirect ar-gument, tightly bound to the MSSM. In fact the model-dependence of the little hierarchyproblem is clear when one moves away from the MSSM, as it has been shown in the recentyears. For example, the addition of a gauge singlet, as in the NMSSM (see [33] and thereferences therein), can contribute to the Higgs quartic coupling and raise the Higgs masswithout introducing fine-tuning [34, 35]. On the other hand new physics can modify theHiggs boson decays in ways that weaken the LEP-2 limit (see the references within [36] andmore recently [37]).On the contrary, the LHC has the potential to probe fine-tuning in a model-independentway by directly placing limits on the superpartner masses. The LHC experiments havealready presented strong limits on the squarks of the first two generations, constraining themto be heavier than m ˜ q > ∼ − − . We cross-checked our results using two different approaches: (1) thefast simulation package PGS [39], which includes a crude detector simulation with smearing,and (2) our own new pipeline, tentatively called ATOM [40], which uses truth level objectsand corrects for efficiencies of leptons, photons, and b-jets. The two pipelines are validatedagainst the experimental results of all the analyses that we consider, and their results agreewith each other. By using the event yields presented in the experimental papers, we canderive “theorist’s limits” on natural SUSY, i.e. , estimates of what could be excluded byfull experimental studies. Our results provide the benefit of showing which, among thecurrent searches, sets the strongest limits and what are the weaknesses and strengths of theexisting analyses. Such information could be used as a starting point for future experimentalinvestigations.In this work, as we will see, we find that the LHC now has the reach to begin to probethe direct production of stops, in certain cases. There is also the reach to probe the left-handed sbottom, who also must be light because of the Standard Model (SM) weak isospinsymmetry. The reach for gluinos decaying to stops and sbottoms is clearly larger, givenits larger production cross-section. While, a priori , the gluino mass is less constrained bynaturalness than the stop mass because it only contributes to the Higgs potential at two loops,we will see that the limits on the gluino are now comparably important, for naturalness, asthe limits on stops, given the larger gluino cross-section. At the same time we find no reachyet to directly probe the higgsino mass beyond the LEP-2 limit on charginos [41].A number of studies have already considered the implications of the LHC results for5USY. On one side there have been studies interpreting the results in terms of specific UVmodels, such as CMSSM/mSUGRA with 35 pb − [42] and 1 fb − [43], and anomaly mediationwith 1 fb − [44], focusing on characteristic theory-based slices of the soft breaking parameterspace. On the other side, there have been bottom-up studies based on broad parameterscans with 35 pb − [45] and 1 fb − [46], trying to cover the whole MSSM parameter spacesystematically, agnostic of any theoretical bias.Our approach differs in that it is decidedly bottom-up, but more focused than broadscans which are penalized by the “curse of dimensionality” of the SUSY parameter space.We determine the limits on superpartner masses specified in terms of soft parameters atthe electroweak scale. We restrict the dimensionality of the parameter space by adopting asimplified model philosophy [47], which is to decouple the states that are not relevant for thesignature of interest. Our choices of simplified models are carefully motivated by naturalnessbecause the states that we keep light are required by fine-tuning to be light and the statesthat we decouple are unrelated to naturalness [28], as summarized in Fig. I.The structure of the paper is as follows. In Section 2, we review in more detail the impli-cations of natural electroweak symmetry breaking in SUSY and we derive the implicationsfor the sparticle spectrum. We remark on the little hierarchy problem and the growing pref-erence for flavor dependent supersymmetry breaking. In Section 3, we review the currentstatus of supersymmetry searches, focusing on the results relevant for our discussion on natu-ralness. Section 4 contains the main results of our paper: our estimated limits on the massesof stops and gluinos. In Section 5, we interpret our results in the context of specific models,such as the MSSM, scenarios with gaugino unification or those with Minimal Flavor Viola-tion (MFV). We conclude in Section 6, briefly summarizing our findings. The appendicescontain a detailed description of ATOM and our validation procedure, and a brief discussionabout the challenge of estimating the future reach of the searches we have considered. II. SUSY NATURALNESS PRIMER
In this section we review the basic arguments that determine the minimal set of require-ments for natural ElectroWeak Symmetry Breaking (EWSB) in a supersymmetric theory.The subject has received a lot of attention in the past decades [24–26]. Here we will recollect6 H ˜ t L ˜ b L ˜ t R ˜ g natural SUSY decoupled SUSY ˜ W ˜ B ˜ L i , ˜ e i ˜ b R ˜ Q , , ˜ u , , ˜ d , FIG. 1: Natural electroweak symmetry breaking constrains the superpartners on the left to belight. Meanwhile, the superpartners on the right can be heavy, M (cid:29) the main points, necessary for the discussions of the following sections. In doing so, we willtry to keep the discussion as general as possible, without committing to the specific Higgspotential of the MSSM. We do specialize the discussion to 4D theories because some aspectsof fine tuning can be modified in higher dimensional setups.In a natural theory of EWSB the various contributions to the quadratic terms of the Higgspotential should be comparable in size and of the order of the electroweak scale v ∼
246 GeV.The relevant terms are actually those determining the curvature of the potential in thedirection of the Higgs vacuum expectation value. Therefore the discussion of naturalness7an be reduced to a one-dimensional problem as in the Standard Model, V = m H | H | + λ | H | (2)where m H will be in general a linear combination of the various masses of the Higgs fields withcoefficients that depend on mixing angles, e.g. β in the MSSM. Each contribution, δm H ,to the Higgs mass should be less than or of the order of m H , otherwise various contributionsneed to be finely tuned to cancel each other. Therefore δm H /m H should not be large. Byusing m h = − m H one can define as a measure of fine-tuning [26],∆ ≡ δm H m h . (3)Here, m h reduces to the physical Higgs boson mass in the MSSM in the decoupling regime. Infully mixed MSSM scenarios, or in more general potentials, m h will be a (model-dependent)linear combination of the physical neutral CP-even Higgs boson masses. As is well known,increasing the physical Higgs boson mass ( i.e. the quartic coupling) alleviates the fine-tuning [34, 35].If we specialize to the decoupling limit of the MSSM and approximate the quartic couplingby its tree level value λ ∝ ( g + g (cid:48) ) cos β , then we find that m h = cos β m Z . We thenrecover the usual formula for fine tuning in the MSSM, Eq. 1, in the large tan β limit.In a SUSY theory at tree level, m H will include the µ term . Given the size of thetop quark mass, m H also includes the soft mass of the Higgs field coupled to the up-typequarks, m H u . Whether the soft mass for the down-type Higgs, m H d , or other soft terms inan extended Higgs sector, should be as light as µ and m H u is instead a model-dependentquestion, and a heavier m H d can even lead to improvements [48]. The key observation thatis relevant for SUSY collider phenomenology is that higgsinos must be light because theirmass is directly controlled by µ , µ < ∼
200 GeV (cid:18) m h
120 GeV (cid:19) (cid:32) ∆ − (cid:33) − / (4) It is straightforward to extend this discussion to include SM singlets that receive vevs, see for example [35]. In theories where the µ -term is generated by the vev of some other field, its effective size is genericallybound to be of the order of the electroweak scale by naturalness arguments. For a proof in the NMSSMsee, e.g. , [35].
8t loop level there are additional constraints. The Higgs potential in a SUSY theory iscorrected by both gauge and Yukawa interactions, the largest contribution coming from thetop-stop loop. In extensions of the MSSM there can be additional corrections, e.g. comingfrom Higgs singlet interactions in the NMSSM, which can be important for large values ofthe couplings. The radiative corrections to m H u proportional to the top Yukawa couplingare given by, δm H u | stop = − π y t (cid:16) m Q + m u + | A t | (cid:17) log (cid:18) ΛTeV (cid:19) , (5)at one loop in the Leading Logarithmic (LL) approximation (which is sufficient for thecurrent discussion), see e.g. [49]. Here Λ denotes the scale at which SUSY breaking effectsare mediated to the Supersymmetric SM. Since the soft parameters m Q , m u and A t controlthe stop spectrum, as it is well-known, the requirement of a natural Higgs potential sets anupper bound on the stop masses. In particular one has (cid:113) m t + m t < ∼
600 GeV sin β (1 + x t ) / (cid:32) log (Λ / TeV)3 (cid:33) − / (cid:18) m h
120 GeV (cid:19) (cid:32) ∆ − (cid:33) − / , (6)where x t = A t / (cid:113) m t + m t . Eq. 6 imposes a bound on the heaviest stop mass. Moreover,for a fixed Higgs boson mass, a hierarchical stop spectrum induced by a large off-diagonalterm A t tend to worsen the fine-tuning due to the direct presence of A t in the r.h.s. of eq. 5.All the other radiative contributions to the Higgs potential from the other SM particlespose much weaker bounds on the supersymmetric spectrum. The only exception is thegluino, which induces a large correction to the top squark masses at 1-loop and thereforefeeds into the Higgs potential at two loops. One finds, in the LL approximation, δm H u | gluino = − π y t (cid:18) α s π (cid:19) | M | log (cid:18) ΛTeV (cid:19) , (7)where M is the gluino mass and we have neglected the mixed A t M contributions that canbe relevant for large A-terms. From the previous equation, the gluino mass is bounded fromabove by naturalness to satisfy, M < ∼
900 GeV sin β (cid:32) log (Λ / TeV)3 (cid:33) − (cid:18) m h
120 GeV (cid:19) (cid:32) ∆ − (cid:33) − / . (8)In the case of Dirac gauginos [50] there is only one power of the logarithm in Eq. 7, amelio- The other logarithm is traded for a logarithm of the ratio of soft masses. We assume that the new log is O (1), but in principle it can be tuned to provide further suppression. / TeV)) / and leading to a bound of roughly 1 . M , M ) < ∼ (3 TeV ,
900 GeV) (cid:32) log (Λ / TeV)3 (cid:33) − / (cid:18) m h
120 GeV (cid:19) (cid:32) ∆ − (cid:33) − / . (9)The bino is clearly much less constrained, while the wino is as constrained as the gluino, butonly for low-scale mediation models. For the squarks and sleptons there is only a significantbound from the D-term contribution, if Tr( Y i m i ) (cid:54) = 0, and it is generically in the 5 −
10 TeVrange.In the MSSM, the upper bound on the stop mass from the requirement of natural EWSB isin tension with the lower bound on the Higgs boson mass, set by the LEP-2 experiments. Thephysical Higgs boson mass is controlled by the quartic coupling and the relevant radiativecorrections are [51, 52] δm h = 3 G F √ π m t (cid:32) log (cid:32) m t m t (cid:33) + X t m t (cid:32) − X t m t (cid:33)(cid:33) (10)with m ˜ t the average stop mass and X t = A t − µ cot β , where µ is the supersymmetric Higgsmass parameter. Since at tree level m h ≤ m Z , requiring m h > ∼
114 GeV translates into alower bound on the average stop mass of about 1 . X t (cid:28) m ˜ t and about 250 GeV for X t = √ m ˜ t , where the stop contribution to the Higgs mass is maximized.Before the start of the LHC this was the strongest, though indirect, lower bound on thestop masses and the main source of fine-tuning for the MSSM. However, this lower boundon the stop masses does not necessarily apply to generalizations of the MSSM. In fact, as in, e.g. , the NMSSM [33], an extended Higgs sector can easily lead to new contributions to theHiggs quartic coupling, raising the Higgs mass above the LEP limit without the necessity ofhaving very heavy stops [34].On the other hand, Eq. 5 holds generically, and one can address the question of thenaturalness of the electroweak scale in light of direct sparticle searches, independently of thesearches for the Higgs boson(s) .Let us now summarize the minimal requirements for a natural SUSY spectrum: An extended structure of the Higgs sector will also modify the spectrum of the neutralinos and charginos,and change their relative branching ratios into gauge bosons vs. Higgses. These effects can modify, in two stops and one (left-handed) sbottom, both below 500 −
700 GeV. • two higgsinos, i.e. , one chargino and two neutralinos below 200 −
350 GeV. In theabsence of other chargino/neutralinos, their spectrum is quasi-degenerate. • a not too heavy gluino, below 900 GeV − . increases the fine-tuning in the Higgs potential.In particular, at one loop one has, δm H (cid:39) (cid:16) m Q − m Q , (cid:17) (cid:39) (cid:16) m U − m U , (cid:17) , (11)where the squark mass splittings pose a lower bound on the amount of fine-tuning. Theimplications of the LHC results on this class of models will be further discussed in Section V. general, the phenomenology of SUSY searches. However the modifications caused by an extended Higgssector are most important for searches looking at direct electroweak-ino production, which is beyond theLHC capabilities with 1 f b − . We therefore neglect this issue in the rest of the paper. II. CURRENT STATUS OF SUSY SEARCHES
In this section we will study the consequences of the first one and a half years of LHCresults on supersymmetry. The most relevant analyses performed by the ATLAS and CMScollaborations are listed in Table I, based on approximately 1 f b − of luminosity from the2011 dataset. The list contains mostly searches for SUSY, but also some exotica searchesthat were not used to set limits on SUSY, highlighted in blue. Some of the analyses havenot been included in this work because they appeared while this work was being completed,and are highlighted in red.Let us first summarize the results presented by the two collaborations in their papers.This will set the stage for the more general investigation of the natural SUSY parameterspace described in the previous section, which will be performed in Section IV.The performance of nearly all of the SUSY analyses are compared within the standardCMSSM m − m / plane. Here, the most stringent constraints come from the jet + /E T searches, and provide limits of m / > ∼
540 GeV for low m and m / > ∼
300 GeV for large m , corresponding to squark masses of ∼ . m ˜ q = M Q , = M D , = M U , and m ˜ g , with m χ = 0, thus maximizing the multiplicityof squarks and loosing the dependence of the bounds on the neutralino mass. CMS insteadpresents two separate plots, one for squark pair production, with each squark decaying intoa quark and a neutralino, the other for gluino pair production, with each gluino three-bodydecaying into two quarks and a neutralino, using ( m ˜ q , m χ ) and ( m ˜ g , m χ ) as parameters,with all the other states decoupled. This can allow the exploration of more general squarkspectra and shows the dependence on the neutralino mass, but at the same time misses theassociated squark-gluino production relevant when m ˜ q ∼ m ˜ g , which is instead captured bythe ATLAS presentation. Nevertheless, in both cases one can easily extrapolate the availableinformation. One finds that squarks and gluinos decaying hadronically are constrained to be12 TLAS CMSchannel L [fb − ] ref. channel L [fb − ] ref.jets + /E T α T H T , /H T b -jets (+ l’s + /E T ) 1 b, b m T (+ b ) 1.1 [13] b + 1 l b, b b (cid:48) b (cid:48) → b + l ± l ± , l t (cid:48) t (cid:48) → b + l + l − /E T ) 1 l l µ ± µ ± t ¯ t → l t ¯ t → l Z → l + l − l l, l + /E T l l, l − , for signatures that are produced bymodels of natural supersymmetry. We have categorized the searches into three categories, (1) fullyhadronic, (2) heavy flavor, with or without leptons, and (3) multileptons without heavy flavor. Thesearches with blue labels have not been used by experimentalists to set limits on supersymmetry,but we have included them because they overlap with SUSY signature space. We have simulatedall of the above searches and included them in our analysis, with the exception of the searches withred labels, which were released while we were finalizing this study. We explored the possibility ofusing the CMS search for t (cid:48) in the lepton plus jets channel [23], however this search uses a kinematicfit on signal plus background and does not report enough information for us to extrapolate this fitto other signals. at or above 900 GeV − α T search [11] sets a lower limit of 500 GeV on m ˜ q for m ˜ q − m χ = 200 GeV and decoupled gluino. Clearly this is an important point: a quasi-degenerate squark spectrum around 500 GeV with µ = 300 GeV is only moderately tuned,and does not necessitate the introduction of any splitting between the first/second and thethird generation squarks. The question here is how heavy must the gluino be for this resultto hold, and whether or not other searches impose stronger constraints on the squark masses.We will address this issue in Sect. V.Let us now move to briefly discuss the searches requiring b-jets. These includes bothSUSY and exotica ( t (cid:48) ) searches. Different analyses require different numbers of leptons inthe final state and/or the presence of /E T . In particular, the CMS M T analysis [13] is alooser jets+ /E T search where the cuts on the hadronic activity H T and the /E T have beenrelaxed in favor of the requirement of a b-jet. ATLAS, on the other hand, has presentedtwo analyses, tailored at gluino pair production with gluinos decaying either to sbottoms [3]or to stops [4], requiring 0 or 1 leptons, respectively. They also present their results interms of simplified models, parameterized by gluino and sbottom (stop) masses or, in caseof [4], gluino/neutralino masses for a simplified model where the gluino decays three-body,˜ g → t ¯ tχ . One can see that their limits are driven by gluino pair production and that theydisappear for a sufficiently heavy gluino, m ˜ g > ∼ −
600 GeV. On the other hand it is notclear whether other searches of Table I also have the power to constrain these scenarios andwhat is their reach. This is the main motivation for the study of the next section, where wewill consider the constraints on stops and stops+gluino, decaying into higgsinos (and/or abino).Finally various multi-lepton searches with and without missing energy have the power toconstrain scenarios involving decays into tops and gauge bosons, since these states may yieldleptons in the final state. With leptons, the SM backgrounds are considerably smaller thanthose for the jets+MET searches. Therefore it is interesting to see whether these analysesare relevant for constraining natural SUSY spectra. Unfortunately this information cannoteasily be extracted from the experimental papers, where most of the results are expressedas CMSSM exclusion regions or in simplified models involving first two generation squarks14gluinos) decaying into charginos and neutralinos. Therefore we will investigate the reachof these searches for natural SUSY spectra involving third generation squarks in the nextsection.An important set of searches relevant for the limits on third generation squarks are thoselooking for Heavy Stable (or long-lived) Charged/Colored Particles (HSCPs). Both AT-LAS [54, 55] and CMS [56, 57] have performed searches for HSCPs, and the current moststringent limits are around 600 GeV for stop LSP, which already constitutes moderate fine-tuning. Therefore in the next section we will not consider the possibility of a long-livedstop/sbottom at the bottom of the SUSY spectrum. Instead, we will always assume thateither a higgsino, or in certain cases a bino (gravitino), is the LSP.Finally, let us comment on the current bounds on direct higgsino production. The mostrobust limit comes from the LEP-2 constraint on chargino pair production and is about100 GeV [41]. Collider searches from the Tevatron do constrain charginos and neutralinosfrom trilepton studies [58], but the Tevatron only improves on the LEP limit when there arelight sleptons in the spectrum, increasing the number of leptons in the final state. On theother hand, the LHC, with less than or about 1 f b − , probably does not have enough lumi-nosity to produce competitive constraints on the direct production of charginos/neutralinos.Since the Tevatron bounds are model-dependent and sleptons are not required to be lightby naturalness, we will only consider, in the next section, higgsinos in association with stops(sbottom) with and without the gluino, and use the LEP-2 limit as a lower bound for thehiggsino masses. IV. THE LIMITS
In this section we present our main results: our estimates of the limits on the masses ofthe superpartners that must be light for natural electroweak symmetry breaking. In orderto avoid excessive fine-tuning, the higgsinos, stops, and gluino must not be too heavy, asdiscussed in Sect. II. We find no LHC limit, with the first 1 fb − , on higgsinos, beyond theLEP-2 limit on the charginos, m ˜ H ± > ∼
100 GeV [41]. We do find that the LHC sets limitson the direct production of third generation squarks, and on the production of gluinos thatdecay through on or off-shell stops and sbottoms. After briefly discussing our methodology,15e present our estimates of the limits on stops in Sect. IV B and on gluinos in Sect. IV C.The LHC experiments have not yet presented limits on the direct production of stopsor sbottoms decaying to a neutralino LSP. And only a handful of searches, looking for b-jets plus missing energy, have presented limits on gluinos decaying through on or off-shellstops and sbottoms [3, 4]. However, many searches have been conducted with 1 fb − , asreviewed in Sect. III, and these searches collectively cover a large signature space. In orderto address the status of naturalness in supersymmetry, we would like to ask the question:do the existing LHC searches, conducted with 1 fb − , set limits on the direct production ofstops and sbottoms? And what is the strongest limit on the gluino mass, when stops arelight? In order to answer these two questions, we have simulated the existing searches andestimated the limits on stops and gluinos. A. Methodology and Caveats
Here, we briefly discuss our methodology for simulating the LHC searches. We calcu-late the SUSY spectrum and the decay tables for SUSY particles with the program SUSY-HIT [59]. Events were simulated using Pythia v. 6.4.24 [60]. We use NLO K-factors, fromProspino v. 2.1 [61], for colored superparticles production. We then pass the events throughtwo different pipelines, allowing us to internally cross-check our results. The first pipeline,Atom [40], uses truth-level objects and will be further discussed in Appendix B. As a secondpipeline, we use PGS [39], which acts as a crude detector simulation including smearing. Aswe discuss in Appendix A, we validate both simulations by reproducing the published limitsof all of the searches. Typically, both Atom and PGS reproduce experimental acceptanceswith an accuracy better than 50%, which results in superparticle mass limits that are nor-mally accurate within about 50 GeV. For searches with multiple channels, we quote thelimit from the channel with the best expected limit, at each point in signal parameter space.All limits are 95% confidence level exclusions using the CL s statistic [62]. The limit on stops or gluinos is normally not very sensitive to a < ∼
50% error in acceptance, because cross-sections are steep functions of masses. An important exception, to keep in mind, arises when the acceptanceis also a steep function of mass, in which case σ × (cid:15) × A may vary more slowly with mass, enhancing thesensitivity of the limit to mis-modeling the acceptance. One of our pipelines, Atom, automatically detectssuch cases, allowing us to identify potential problems.
16n each of the cases considered in the following, we will adopt the simplified model phi-losophy [47], which is to only consider the relevant particles (stop/sbottom and higgsino)and to decouple the rest of the spectrum, in order to highlight the relevant kinematics. Wechoose 3 TeV as the mass scale for the rest of the decoupled superpartners. Throughout thiswork, we fix tan β = 10.We would like to stress a caveat, inherent to “theorist level” extrapolations of LHC limits.It is important to keep in mind that our limits do not represent actual experimental limits.Accurate limit setting requires the full experimental detector simulation, which we do nothave access to, and a careful study of systematic uncertainties of the signal acceptance,which we do not attempt. We are not trying to replace these important steps. Rather,the limits we quote should be viewed as representative estimates of what we believe willbe possible to exclude, if the experimentalists apply the current searches to study naturalsupersymmetric spectra. We have identified parameter spaces that are useful for assessingthe status of naturalness in supersymmetry, and we hope the task of setting more accuratelimits on natural supersymmetry will now be taken up by our experimental colleagues. B. Stop Limits
Stops must be light if electroweak symmetry breaking is natural, because they contributeto m H u at one-loop order. As we discuss in this section, we have found that the existing LHCsearches in certain cases place limits on the direct production of stops. These limits beingas strong as m ˜ t > ∼
300 GeV, show that the null results of the LHC are starting to directlyprobe SUSY naturalness. Note, that loops of light stops can modify the higgs productioncross-section and branching ratios (see [63] and references therein), and for some choices ofparameters, there can be an increase of σ gg → h × Br( h → γγ ). This means that LHC Higgssearches can also be used to provide indirect limits on light stops. We do not consider suchindirect limits here, since they rely on model-dependent assumptions about the Higgs sector,and we instead choose to focus on the direct limits on stop production.Before starting to review the limits, let us recall how the stop masses are determined bysoft supersymmetry breaking parameters [49]. In general, left and right-handed stops mix,17nd the squared stop soft masses are given by the eigenvalues of the following matrix, m Q + m t + t L m Z m t X t m t X t m U + m t + t R m Z , (12)where m Q and m u are the left and right-handed stop soft masses, respectively, X t = A t − µ/ tan β determines the left-right stop mixing, and t L,R parameterize D -term correctionsthat are introduced by electroweak symmetry breaking. The D -term coefficients are givenby t L = (1 / − / θ W ) cos 2 β and t R = 2 / θ W cos 2 β .As explained before, naturalness also requires a light left-handed sbottom, whose massis also determined by m Q . If tan β is not too large, then left-right sbottom mixing can beneglected and the right handed sbottom is not required, by naturalness, to be light. In thiscase, the left-handed sbottom mass is given by, m b L = m Q + m b − (cid:18)
12 + 13 sin θ W (cid:19) cos 2 β m Z , (13)where the last term corresponds to the D -term contribution to the sbottom mass.We begin by considering the limits on stops, and the left-handed sbottom, with a higgsinoLSP. These are the most important superparticles to be light if supersymmetry is natural.The spectrum, and the relevant decays, are shown in Fig. IV B. We begin, for simplicity, byneglecting left-right stop mixing, X t = 0 (we will relax this assumption below). Then, theright-handed stop mass is determined by m u and the left-handed stop and sbottom havemasses close to m Q , with the left-handed stop a bit heavier than the left-handed sbottom,due to the m t contribution to the upper-left entry of the stop mass matrix (see eq. 12). Asa further simplification, to illustrate the main kinematical features, we separately considerthe limits of the left-handed stop/sbottom, and right-handed stop.The LHC limit on the left-handed stop and sbottom (right-handed stop) is shown to theleft (right) of Fig. 3, respectively. We find that the strongest limit comes from searches forjets and missing energy, which are shown in the plot. There is a stronger limit on the left-handed stop than the right-handed stop, because of the additional presence of a sbottom,in the left-handed case, leading to an overall larger production cross-section than for theright-handed stop. In both cases the limits are set by both stops and bottoms decaying tob-jets and chargino or neutralino respectively.18 H ˜ H ± b ˜ t L ˜ b L b t t ˜ t R t ˜ H ˜ H ± b FIG. 2: Possible decay modes in the simplified model consisting only of a left-handed stop/sbottom,or right-handed stop, decaying to a higgsino LSP. On the left , we show decays of the left-handedstop and left-handed sbottom, whose masses are both determined by m Q . On the right , we showpossible decays of the right-handed stop, whose mass is determined by m u . At this stage, weneglect left-right stop mixing. We comment that near the edge of the limit, the typical acceptance of the jets plus missingenergy searches for this signal is only ∼ O (10 − ). This is the right order of magnitude to seta limit because 200 GeV stops have a production cross-section of about 10 pb, which thenleads to 10’s of events after cuts, in 1 fb − .To understand why the acceptance is ∼ O (10 − ), we consider, as an example, the highmissing energy selection of the CMS jets plus missing energy search [12]. This search demands H T >
350 GeV and /E T >
500 GeV. We find that moderately hard initial state radiationis required for stops and sbottoms in the mass range of 200-300 GeV to pass this cut.The low acceptance is related to the probability to produce sufficiently hard radiation. Inorder to verify that the acceptance is not considerably underestimated due to the fact thatthe additional jets are populated only by the parton shower in events generated by Pythia(with the total cross-section normalized to the NLO value), we have also generated eventsin Madgraph [64] with stop and sbottom pair production including also the possibility ofradiating one extra parton at the level of the matrix element. Overall we find good agreementbetween the two estimates, within our typical uncertainties.19or comparison with the LHC limits, we have also shown in Fig. 3, the strongest limitfrom the Tevatron, which comes from the D . − . This search setslimits on sbottom pair production, with the decay ˜ b → b ˜ N . For the left-handed spectrum,this limit applies directly to the sbottom, which decays ˜ b L → b ˜ H for the mass range ofinterest (the decay to top and chargino is squeezed out). For the right-handed stop, thedominant decay is ˜ t R → b ˜ H ± , which means that the stop acts like a sbottom, from the pointof view of the Tevatron search . We note that the Tevatron limit only applies for higgsinosjust above the LEP-2 limit, m ˜ H <
110 GeV, and we see that the Tevatron has been surpassedby the LHC in this parameter space.
180 200 220 240 260 280 300100120140160180200220240 m t L (cid:142) (cid:64) GeV (cid:68) m H (cid:142) (cid:64) G e V (cid:68) Left (cid:45)
Handed Stop (cid:144)
Sbottom
ATLAS 2 (cid:45) (cid:45) CMS Α T , 1.14 fb (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) D0 b (cid:142) b (cid:142) , 5.2 fb (cid:45) m b L (cid:142) (cid:61) m H (cid:142)
160 180 200 220 240100120140160180200220240 m t R (cid:142) (cid:64) GeV (cid:68) m H (cid:142) (cid:64) G e V (cid:68) Right (cid:45)
Handed Stop
ATLAS 2 (cid:45) (cid:45) CMS Α T , 1.14 fb (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) D0 b (cid:142) b (cid:142) , 5.2 fb (cid:45) m t R (cid:142) (cid:61) m H (cid:142) FIG. 3: The LHC limits on the left-handed stop/sbottom ( left ) and right-handed stop ( right ), witha higgsino LSP. The axes correspond to the stop pole mass and the higgsino mass. We find that thestrongest limits on this scenario come from searches for jets plus missing energy. For comparison,we show the D . − (green), which only applies for m ˜ N < ∼
110 GeV, and has beensurpassed by the LHC limits. In order to apply the Tevatron sbottom limit to right-handed stops, we have assumed that the decayproducts of the charged higgsino are soft enough not to effect the selection, which applies when the masssplitting between the charged and neutral higgsino is small
20e now consider the LHC limit on stops and the left-handed sbottom decaying to a bino(or gravitino) LSP. Here we will take the higgsinos to be heavier than the stops, and againwe neglect left-right stop mixing for simplicity, X t = 0. The relevant spectra and decaymodes are shown in Fig. 4. The most important change, versus higgsino LSP, is that there isno light chargino for the stops and sbottoms to decay to. For left-handed stops, this meansthat once the decay to the bino and a top is squeezed out, m ˜ t L < m ˜ B + m t , the left-handedstop dominantly decays to the sbottom through a 3-body decay, ˜ t L → W ∗ ˜ b L . For the righthanded stop, once the two body decay is unavailable, m ˜ t R < m ˜ B + m t , the dominant decayis a three-body decay through an off-shell top. And once the mass splitting between thestop and the bino is less than the W mass, the dominant decay is 4-body with the top andthe W both off-shell. The right-handed stop decays are challenging to constrain because thefinal states are similar to the t ¯ t background. The same decay modes apply both for bino andgravitino LSP, the only relevant difference is that the bino mass is a free parameter, whereasthe gravitino must be light, m ˜ G < ∼ keV for decays to occur within the detector. ˜ t R t ˜ B ( ˜ G ) t ˜ t L ˜ b L W ∗ b ˜ B ( ˜ G ) FIG. 4: Possible decay modes of the left-handed stop/sbottom ( left ), or right-handed stop ( right ),to a bino or gravitino LSP. Higher body final states occur when the mass splittings squeeze out thetwo-body decays of the stops, m ˜ t L,R < m ˜ B − m t . We present our estimate of the limit on the left-handed stop/sbottom with bino LSP inFig. 5. The limit with a gravitino LSP can be inferred by looking along the m ˜ B ≈ ∼
350 GeV for light bino, where more phase space is available.For the right-handed stop decaying to a bino, we show no plot because we find no limitabove m ˜ t R > ∼
200 GeV. We do find that there may be marginal sensitivity for stop massesaround 200 GeV. This marginal sensitivity comes from searches for jets plus missing energy,Z plus jets plus /E T and from searches for top partners. We do not show an estimate for thelimit on right-handed stops with masses near the top mass because the signal topology isvery similar to the t ¯ t background. This means that any limit extrapolation is sensitive to thedetailed systematics of the top background, and we believe this parameter regime requiresfurther dedicated study.We conclude our discussion of limits on stop production by considering the limit on bothleft and right-handed stops, including left-right mixing. By inspecting the stop mass matrix,eq. 12, we see that there are two ways to change the relative stop masses, which are depictedin Fig. 6. The first way is to assign different soft masses for the left and right-handed stops,as shown to the left, and center of Fig. 6. In the limit of no left-right mixing, the left-handedsbottom and left-handed stop masses will both be close to the value of m Q (up to m t and D -term corrections). The second way to change the stop masses is to introduce left-rightstop mixing, | X t | >
0, shown to the right of Fig. 6. When there is large left-right mixing,the sbottom mass is no longer required to be close to one of the stop masses.We have chosen a parameter space designed to study how the LHC limit depends on left-right stop mixing. We fix the value of m Q + m u = (450 GeV) , which fixes the amount offine-tuning introduced by the stop masses into δm H u . Then, we separately vary the differenceof the left-right stop soft masses, m Q − m u , and the left-right mixing, X t . We show how thelightest stop mass and sbottom mass depend on these parameters in Fig. 7. The sbottommass increases with m Q , moving from left to right across the plot. Meanwhile, the lighteststop mass decreases as either the stop mixing is increased, or as the difference of the stopsoft masses is increased.We show our LHC limit for this parameter space in Fig. 8. Here, we have chosen a higgsinoLSP with a mass of 100 GeV. We note that left-right stop mixing can allow decays between22
50 200 250 300 350 400050100150200250 m t L (cid:142) (cid:64) GeV (cid:68) m B (cid:142) (cid:64) G e V (cid:68) Left (cid:45)
Handed Stop (cid:144)
Sbottom
ATLAS 2 (cid:45) (cid:45) CMS Α T , 1.14 fb (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS M T2 , 1.1 fb (cid:45) D0 b (cid:142) b (cid:142) , 5.2 fb (cid:45) m b L (cid:142) (cid:61) m B (cid:142) FIG. 5: The LHC limits on left-handed stop/sbottom, with a bino LSP. The axes correspondto the stop pole mass and the bino mass. The limit with a gravitino LSP in place of the binocan be inferred from looking at the line with m ˜ B ≈ . We find that searches for jets plusmissing energy set the strongest limits, which surpass the D . − (green). Wedo not show the case with a right-handed stop with bino/gravitino LSP, where we find no limitabove m ˜ t > ∼
200 GeV. We find that there may be marginal sensitivity for lighter right-handedstops, although this requires further investigation due to the similarity of the stop signal and theirreducible top background. the stops to a Higgs boson, ˜ t → ht . These decays are clearly more model dependent sincewe do not have much information on the structure of the Higgs sector yet. For concreteness,we have fixed m h = 120 GeV and take the decoupling limit in the Higgs sector, m A (cid:29) m Z .The strongest limit in this parameter space comes again from searches for jets plus missingenergy, and the outer parts of the plot are excluded. This is simple to understand: theexclusion corresponds to the part of parameter space where the lightest stop mass fallsbelow the limit, m ˜ t > ∼ −
250 GeV. The limits are stronger to the left side of the plot,because this is the part of parameter space where the sbottom is also light. As can beinferred from Fig. 3, changing the values of the higgsino mass in the 100 −
200 GeV range23 t L ˜ b L ˜ t R m Q − m u > X t = 0 ˜ t L ˜ b L ˜ t R m Q − m u < X t = 0 ˜ b L | X t | > ˜ t ˜ t FIG. 6: Different ways that stops can be split and mixed. The left and right-handed stop polemasses can be split by choosing different soft terms, m Q (cid:54) = m u , as shown to the left and center .The stop masses can also be split due to left-right stop mixing, which is controlled by the parameter X t , as shown to the right . The left-handed sbottom mass is determined only by m Q , in the limitthat left-right sbottom mixing can be ignored, which we assume here. do not significantly modify the structure of the bound.We do not consider here the case of a bino LSP for the reasons already explained abovefor ˜ t R → ˜ B decays. C. Gluino Limits
In this section, we add the gluino to the mix and consider the LHC limits, after 1 fb − , ongluinos decaying through on or off-shell stops and sbottoms. Recall from the discussion inSect. II that the gluino mass is also important for naturalness because it corrects the Higgspotential at 2-loop order. In this section, we will find that the gluino is constrained to beheavier than about 600 −
800 GeV. This means, from the point of view of naturalness, thatthe gluino mass limit is as important as the limits on stops discussed in Sect. IV B.24 (cid:45)
200 0 200 400 (cid:45) (cid:45) (cid:45) m Q (cid:45) m u (cid:64) GeV (cid:68) X t (cid:64) G e V (cid:68) m Q (cid:43) m U (cid:61) (cid:72)
450 GeV (cid:76) m b L (cid:142) m t (cid:142)
100 100 100100200300400500200 300 400 500 600 700 (cid:45) (cid:45) (cid:45)
200 0 200 400 600 (cid:45) (cid:45) m Q (cid:45) m u (cid:64) GeV (cid:68) X t (cid:64) G e V (cid:68) m Q (cid:43) m U (cid:61) (cid:72)
700 GeV (cid:76) m b L (cid:142) m t (cid:142) FIG. 7: The masses of the lightest stop, ˜ t , and left-handed sbottom, ˜ b , while varying the stopmixing parameter, X t , and the difference of the left and right-handed soft terms, m Q − m u . Herewe take m Q + m u = (450 GeV) on the left , and (700 GeV) on the right . Fixing this combinationkeeps constant the amount of fine-tuning introduced by the stop soft masses. Moving from left toright, the sbottom mass increases with m Q . Meanwhile, the lightest stop mass decreases movingradially outward in the plot, due to different left-right soft masses in the horizontal direction, andleft-right mixing in the vertical direction. We consider the limits on several different types of spectra, summarized in Fig. 9, involvinggluinos and light stops. Throughout this section, for simplicity we neglect left-right stopmixing by taking X t = 0. A non-zero X t will have minor effects on the region of parameterspace where the bounds are dominated by gluino pair production, and will have the effectof weakening the bounds, to the levels already studied in the previous Section, when gluinosare too heavy to be relevant. Higgsino LSP.
The first type of spectrum we consider, shown to the upper left of Fig. 9,consists of a higgsino LSP, a light gluino, and light stops. This spectrum constitutes theminimal ingredients that must be light for natural supersymmetry. We choose to fix thehiggsino mass to 200 GeV and vary separately the gluino mass and the mass of the stops,25 (cid:45) (cid:45)
100 0 100 200 300 400 (cid:45) (cid:45) (cid:45) m Q (cid:45) m u (cid:64) GeV (cid:68) X t (cid:64) G e V (cid:68) Split (cid:144)
Mixed Stops
ATLAS 2 (cid:45) (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS Α T , 1.14 fb (cid:45) allowed m Q (cid:43) m U (cid:61) (cid:72)
450 GeV (cid:76) FIG. 8: The limit on the stops and left-handed sbottom, including stop mixing. We take m Q + m u = (450 GeV) , which fixes the amount of fine-tuning that the stop soft masses introduce toelectroweak symmetry breaking. We vary the stop mixing, X t , and the difference of the stop softmasses, m Q − m u . The resulting stop / sbottom mass spectrum is shown in Fig. 7. The strongestlimits come from searches for jets plus missing energy, which exclude the region outside of thecircular exclusion contour. This is the part of parameter space where one stop becomes light, asshown in Fig. 7. The green band to the left of the plot is excluded by the D . − . which we take to be degenerate, m Q = m u . The limit that we find on this spectrumis shown to the left of Fig. 10. For readability, we only show a selection of limit curves,including the searches that set the strongest limits.In the high gluino mass region of the higgsino LSP parameter space, we find that thestrongest limit comes from the CMS search for jets plus missing energy, m ˜ t i > ∼
300 GeV.26 H ˜ t L,R ˜ b L ˜ g ˜ H ˜ t L,R ˜ b L ˜ B ˜ g ˜ H ˜ B ˜ t L , ˜ b L ˜ t R ˜ g ˜ H ˜ t L,R ˜ b L ˜ B ˜ q , higgsino LSP bino LSPsplit stops un-decoupled squarks ˜ g FIG. 9: The four benchmark scenarios that we use to study limits on gluinos and stops. In the higgsino LSP scenario, we consider a gluino, degenerate stops and left-handed sbottom, and ahiggsino LSP. These are the minimal ingredients that need to be light for naturalness, and forsimplicity we decouple the rest of the spectrum. In the bino LSP scenario, we add a bino with asoft mass of M = 100 GeV. In the split stops scenario, we take the right-handed stop to be lightand the left-handed stop/sbottom to be heavier than the gluino. In the un-decoupled squarks scenario, we test how the limit strengthens by lowering the mass of the first two generation squarks. This is consistent with the limit we found on stops with a higgsino LSP in Fig. 3 of Sect. IV B,with the limit strengthened slightly because of the simultaneous presence of the left-handedstop/sbottom and the right-handed stop. In the heavy stop part of the parameter space,27e find that the strongest limit comes from the CMS M T version of the jets plus missingenergy search, and from the ATLAS search for 1 lepton plus jets and missing energy. Here,the lepton comes from the decay of a top produced in the gluino decay, through an on oroff-shell stop (˜ g → t + t − ˜ H ) or sbottom (˜ g → t ± b ± ˜ H ∓ ). We also find that the CMS searchfor jets plus missing energy may set the strongest limit along the line where the sbottomis slightly lighter than the gluino, m ˜ b ∼ m ˜ t i < ∼ m ˜ g . Here, the gluino decays to a soft b-jetplus a sbottom, which can decay to a very hard b-jet and a neutral higgsino, ˜ b ± → b ± ˜ H .The presence of two very hard jets in the final state leads to a high acceptance for the jetsplus missing energy search. However, we find that the acceptance in this regime is verysensitive to the precise value of the missing energy cut. This prevents us from making arobust statement about the exclusion (hence the dashed line in the plot), after accountingfor the uncertainties of our simulations. Bino LSP.
Second, we consider the limit on gluinos and stops with a bino LSP at 100GeV and a higgsino at 200 GeV, as shown to the upper right of Fig. 9. One motivation foradding a bino is that it allows for mixed bino/higgsino dark matter. From the kinematicspoint of view, the interesting effect is that the bino lengthens the supersymmetric cascades.Typically, the stops will decay first through the higgsinos (because the top Yukawa is strongerthe hypercharge gauge coupling), which then decay to the bino, ˜ H ± → W ± ˜ B , ˜ H → Z ˜ B ,through the higgsino/bino mixing angle. The limit on the bino LSP spectrum is shown tothe right of Fig. 3. Once again, searches for jets plus missing energy set the strongest limiton the stop mass, in the large gluino mass limit.The important difference between the bino and higgsino LSP scenarios is that thestrongest limit on the gluino mass, m ˜ g > ∼
700 GeV, comes from searches from same-signdileptons plus missing energy. There are two searches of this type conducted by CMS thatset comparable limits, one supersymmetry search [18] and one search looking for pair pro-duction of b (cid:48) decaying to tops and W ’s [15]. The reason that same-sign dileptons becomea powerful probe with the addition of the bino, is that leptons are produced both by thedecays of tops and by the decays of leptonic W ’s produced when the charged higgsino decaysto the bino. We find no limit from same-sign dileptons when the sbottom mass is loweredsuch that it can no longer decay to a top and a chargino, m ˜ b L ∼ m ˜ t i < m ˜ H + m t , reducingthe number of leptons in the final state. As the stop/sbottom mass is further lowered, the28imit is recovered because ˜ g → ˜ t ± i t ∓ opens up. The result, in our parameter space, is a gap insame-sign coverage from m ˜ t i ∼ m ˜ b l ≈ −
400 GeV. Our choice of µ changes the positionof this gap, but does not affect the overall limit since the search for jets plus missing energycovers this gap and sets the strongest limit in this regime.
400 600 800 1000 1200300400500600700800900 m g (cid:142) (cid:64) GeV (cid:68) m t i (cid:142) (cid:64) G e V (cid:68) Higgsino LSP
Μ (cid:61)
200 GeV
CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS M T2 , 1.1 fb (cid:45) ATLAS 1l, 1.04 fb (cid:45) ATLAS b, 0.83 fb (cid:45)
400 600 800 1000 1200300400500600700800900 m g (cid:142) (cid:64) GeV (cid:68) m t i (cid:142) (cid:64) G e V (cid:68) Bino LSP
Μ (cid:61)
200 GeV M (cid:61)
100 GeVCMS H T (cid:144) MET, 1.1 fb (cid:45) CMS SS, 0.98 fb (cid:45) CMS b', 1.34 fb (cid:45) ATLAS b, 0.83 fb (cid:45) ATLAS b (cid:43) l, 1.03 fb (cid:45) (cid:72) (cid:43) expected (cid:76) FIG. 10: The limits on the
Higgsino LSP and bino LSP scenarios, represented in terms of thegluino mass versus the degenerate stop pole masses. In the limit of large gluino mass, we find thatthe strongest limit on direct stop/sbottom production, m ˜ t > ∼
300 GeV, comes from searches for jetsplus missing energy. With only a higgsino LSP, the strongest limit on the gluino, m ˜ g > ∼
650 GeVcomes from searches for jets plus missing energy, and an ATLAS search for a single lepton plus jetsand missing energy. When both the bino and higgsino are light, we find that the strongest limit, m ˜ g > ∼
700 GeV comes from the CMS search for same-sign dileptons plus missing energy. To the left,the dashed blue line indicates a region of parameter space, m ˜ t < ∼ m ˜ g , that may also be excludedby the CMS search for jets plus missing energy. However, the acceptance is highly sensitive to theprecise value of the missing energy cut in this regime, signaling that the we cannot make a robuststatement, given the precision of our simulation, in this part of parameter space. A somewhat squashed spectrum.
Next, we deform the bino LSP spectrum by squash-ing the mass splitting between the gluinos and the higgsino/bino. Compressing the spectrum29as the impact of reducing the amount of visible and missing energy, typically resulting inweaker limits on superpartner masses [65]. However, it should be kept in mind that the com-pression itself may be a new form of tuning (in the form of a relation between the coloredsuperpartner and LSP mass) depending on the UV completion, therefore it is not totallyclear whether or not compressed MSSM spectra are really more natural (extending the fieldcontent beyond the MSSM, small mass splittings can occur naturally, see for example [66]).In the previous case, we fixed the bino and higgsino masses to 100 and 200 GeV, respec-tively, while varying the gluino and stop masses. Now, we hold constant the splitting betweenthe gluino mass and the bino/higgsino, choosing M = M −
300 GeV and µ = M −
150 GeV.The resulting limits are shown to the left of Fig. 11. The compression has the effect ofsqueezing out many of the decay modes involving tops, for example the three-body decays˜ g → t − t + ˜ H ( ˜ B ) are now kinematically disallowed. This reduces the number of leptons inthe final state, and the strongest limits on the gluino mass, m ˜ g > ∼
600 GeV, now come fromsearches for jets (with and without b-jets) and missing energy.
Split Stops.
We now consider the effect on the gluino mass limit when the stop massesare no longer degenerate, as shown in the lower left of Fig. 9. We vary the gluino mass andthe right-handed stop mass, keeping the left-handed stop/sbottom heavier than the gluino, m Q = 1 . M . While this choice is less justified by naturalness arguments, it is an interestingcase to consider because it highlights different final states with different kinematics. Thebino and higgsino masses are chosen, as in the squashed spectrum considered above, to trackthe gluino mass, M = M −
300 GeV and µ = M −
150 GeV. The most interestingfeature of the split stop case is that, when the two-body decay of the gluino to the stopand a top is kinematically forbidden, m ˜ t R > m ˜ g − m t , the gluino dominantly decays througha top/stop loop to a gluon and a neutral higgsino or bino, ˜ g → g ˜ H ( ˜ B ) [67], as shownin the Feynman diagram to the left of Fig. 12. We have used the program SDECAY [59]to compute the branching ratio of this decay in the parameter space we consider, and wefind that it typically dominates over the three-body decay through the off-shell sbottom,˜ g → b + b − ˜ H ( ˜ B ), as shown to the right of Fig. 12.The limit on the gluino mass, with split stops, is shown to the right of Fig. 11. There aretwo important regimes, depending on whether or not the two body decay of the gluino to atop and the stop is open. When m ˜ t R < m ˜ g − m t , every event contains four tops, and we find30
00 500 600 700 800200300400500600700 m g (cid:142) (cid:64) GeV (cid:68) m t i (cid:142) (cid:64) G e V (cid:68) Somewhat Squashed Spectrum
CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS M T2 , 1.1 fb (cid:45) CMS Α T , 1.14 fb (cid:45) ATLAS b, 0.83 fb (cid:45) m b L (cid:142) (cid:61) m B (cid:142) M (cid:61) M (cid:45)
300 GeV
Μ (cid:61) M (cid:45)
150 GeV
400 500 600 700 800200300400500600700 m g (cid:142) (cid:64) GeV (cid:68) m t R (cid:142) (cid:64) G e V (cid:68) Split Stops m t R (cid:142) (cid:61) m B (cid:142) CMS SS, 0.98 fb (cid:45) CMS M T2 , 1.1 fb (cid:45) CMS Α T , 1.1 fb (cid:45) ATLAS b, 1.14 fb (cid:45) M (cid:61) M (cid:45)
300 GeV
Μ (cid:61) M (cid:45)
150 GeV
FIG. 11: Here we show how the gluino versus stop mass limit changes when the spectrum iscompressed ( left ), or when the stop masses are split ( right ). For the compressed case, we modify the bino LSP benchmark by fixing the mass splitting between the gluino and the LSP to be moderatelycompressed, M − M = 300 GeV, and the limit on the gluino weakens to m ˜ g > ∼ −
600 GeV.For the split stops scenario, the left handed stop/sbottom are taken heavier than the gluino. Themass of the right-handed stop determines which search dominates the gluino mass limit. Same-signdileptons set the strongest limit when ˜ g → t ˜ N i is kinematically allowed. For heavier stops, thedominant gluino decay is the one-loop decay ˜ g → g ˜ N i , and the strongest limit comes from jets plusmissing energy. that same-sign dileptons set the strongest limit, with the leptons coming from top decays.When m ˜ t R > m ˜ g − m t , the one-loop gluino decay dominates, as discussed above, and thestrongest limit comes from the CMS α T version of the search for jets and missing energy.Further raising the stop mass, the three body decay to bottoms becomes competitive withthe one-loop decay, ˜ g → b + b − ˜ H ( ˜ B ), and the strongest limit comes from a channel of theCMS M T search that demands 1 b-jet. Un-decoupled Squarks.
So far, in all of the above benchmarks, we have decoupled thesquarks of the first two generations. This choice was motivated by naturalness, since the31 g ˜ B, ˜ H gt ˜ t R
400 500 600 700 800200300400500600700 m g (cid:142) (cid:64) GeV (cid:68) m t R (cid:142) (cid:64) G e V (cid:68) Br (cid:72) g (cid:142) (cid:174) g N i (cid:142) (cid:76) m g (cid:142) (cid:45) m t R (cid:142) (cid:61) m t m Q (cid:61) M FIG. 12: The dominant decay of the gluino can be the one-loop diagram shown to the left , ˜ g → g ˜ N ,with the stop running in the loop. The branching ratio of this decay path is shown to the right within the parameter space of our split stops benchmark scenario. This decay dominates whenthe right-handed stop is heavy enough to close the two body decay to a top, ˜ g → t ˜ N i , as long as theother squarks are sufficiently heavy to suppress competing three-body decays. For this example,we have taken m Q = 1 . M which is sufficient to suppress the three-body decay mediated by thesbottom, ˜ g → bb ˜ N , relative to the one-loop decay. limits on the gluino and stops are weaker when the squarks of the first two generations areheavy. We conclude our discussion of the limits on gluinos by testing exactly how heavythe squarks need to be. We answer this question by deforming the bino LSP benchmark, asshown to the lower right of Fig. 9. We vary the gluino mass against a common mass chosenfor all of the squarks of the first two generations, m ˜ q = m Q , = m u , = m d , . We fix bothstop soft masses to 520 GeV and, as above, we choose M = 100 GeV and µ = 200 GeV. Thelimit on this scenario is shown in Fig. 13. In the limit of heavy gluino mass, the strongestconstraint comes from searches for jets and missing energy, and the common squark massmust be heavier than about 1 TeV. The strongest limit on the gluino mass comes from same-sign dileptons, as in Fig. 10. As the squark masses are raised, they very quickly decouple,32nd have little effect on the gluino mass once m ˜ q > ∼ .
600 800 1000 1200 1400800900100011001200130014001500 m g (cid:142) (cid:64) GeV (cid:68) m q (cid:142) (cid:64) G e V (cid:68) Un (cid:45) decoupling the other squarks m t i (cid:142) (cid:61)
520 GeV
Μ (cid:61)
200 GeV M (cid:61)
100 GeVCMS SS, 0.98 fb (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS Α T , 1.14 fb (cid:45) ATLAS 1l, 1.04 fb (cid:45) FIG. 13: The limit on the gluino mass versus a common mass for the squarks of the first twogenerations in the un-decoupled squark benchmark. We find that searches for jets plus missingenergy demand that m ˜ q > ∼ . V. IMPLICATIONS FOR SUSY MODELS
In this section we briefly consider some implications of our results for various SUSYmodels. We discuss the interplay of LHC results with the LEP-2 bound on the Higgs massin the MSSM, the consequences of the LHC limits for the flavor structure of the squark softmasses, and finally we will also consider the limit on natural spectra with gaugino unification.We begin this section by discussing how the LHC limits relate to the LEP-2 bound onthe Higgs mass. As we stressed in the introduction and in Sect. II, there are two logicallydifferent reasons why the MSSM may need to be finely-tuned. The first is the little hierarchyproblem which results from the LEP-2 limit on the Higgs mass, and the second is the newset of LHC limits on those superpartners that are relevant for naturalness, like the stops.33o far in this paper, we have focused only on the direct limits without any concern for theHiggs mass, because the little hierarchy problem is model dependent and can be alleviatedby modifications to the Higgs sector of the MSSM, which may or may not substantially affectthe stops and gluino phenomenology. However, it is interesting to ask how these two sourcesof fine-tuning are related without extending the MSSM. The answer to this question is shownin Fig. 14, where we present both the LHC stop limit, derived from our simulations, and thecontours of constant Higgs mass, using the one-loop renormalization improved result of [52].This plot corresponds to higgsino LSP with µ = 100 GeV, tan β = 10, and degenerate stopsoft masses, m u = m Q . We also show the region that is excluded by LEP-2 because oneof the stops is lighter than about 100 GeV, and the region where one of the stops becomestachyonic, due to large left-right stop mixing, leading to charge and color breaking.We have chosen, in Fig. 14, to represent the LHC stop limit, and the Higgs mass contour,in a plane parameterized by the stop A -term and by the square root of the average ofthe left/right stop soft masses squared, (cid:113) m Q + m u . In this parameterization (thanksto Pythagoras) the fine-tuning of the electroweak sector is simply the square of the lineardistance from the origin, as can be easily seen by examining equation 5. We note immediately,by inspecting Fig. 14, that, prior to the LHC, the region of the MSSM with the least fine-tuning was the so-called “maximal mixing” scenario, where X t ∼ A t = √ m ˜ t , because this iswhere the m h = 114 GeV contour passes closest to the origin. We find that this region of theplot is now becoming excluded by LHC searches, showing that there is a complementaritybetween the LHC limits and the LEP-2 limit on the Higgs mass. In other words, the LHC isnow beginning to make the fine-tuning worse in the MSSM. Or more positively stated, theLHC is starting to probe the most interesting part of parameter space that remains in theMSSM. While this statement at the moment strongly depends on having higgsinos lighterthan stops (which is still not absolutely required by naturalness arguments), these resultsare likely to become more robust in the next months.We also show, in Fig. 15, what happens when the stop soft masses are non-degenerate, byfixing m u = 4 m Q . In this case, the LHC carves out a larger region of the parameter spacewhere the Higgs mass satisfies the LEP-2 limit. This behavior can be understood simply.The LHC primarily limits the lightest stop (and the sbottom), whose masses in this case aredetermined by m Q . On the other hand, the radiative contribution to the Higgs mass, and34he fine-tuning which determines the position on the y-axis, is primarily driven by the largeststop soft mass, here m u . The result is that the LHC limit is stronger in the interesting partof parameter space. By comparing figures 14 and 15, we see that naturalness prefers spectrawhere the two stop soft masses are comparable, m u ∼ m Q . (cid:45) (cid:45) A T (cid:64) GeV (cid:68) m Q (cid:43) m u (cid:64) G e V (cid:68) m u (cid:61) m Q Μ (cid:61)
100 GeVTan
Β (cid:61) Charge (cid:144)
Color Breaking LHC, 1 fb (cid:45) LEP t (cid:142) t (cid:142) FIG. 14: Here we show the interplay of the LHC limits that we have found on the stops andleft-handed sbottom with the LEP-2 limit on the Higgs mass. We specialize to higgsino LSP, with µ = 100 GeV. We vary the stop A -term and the square root of the average stop soft mass squared.This unconventional parameterization emphasizes the fine-tuning of the electroweak sector, which,as we discuss in the text, corresponds to the squared distance from the origin of the plot. The redshaded region is the exclusion we find from LHC searches for jets plus missing energy. The greenregion corresponds to a stop lighter than 100 GeV and is excluded by LEP-2. In the blue region,large left-right stop mixing leads to a tachyonic stop and charge/color breaking. The Higgs masscontours emphasize that the LHC is now beginning to probe the region allowed by the LEP-2 Higgsmass exclusion, increasing the fine-tuning in the MSSM. Next we consider the implication of the LHC limits for the flavor structure of the squarksoft masses. Since fine-tuning is determined by the stop soft masses, while the strongest35 (cid:45) A T (cid:64) GeV (cid:68) m Q (cid:43) m u (cid:64) G e V (cid:68) m u (cid:61) m Q Μ (cid:61)
100 GeVTan
Β (cid:61) Charge (cid:144)
Color Breaking LHC, 1 fb (cid:45) LEP t (cid:142) t (cid:142) FIG. 15: The same as Fig. 14, except instead of taking the left/right stop soft masses degenerate, asabove, we fix m u = 4 m Q . This has the impact of increasing the region of the plot that is excludedby the LHC, which sets a limit on the lighter stop and sbottom, whose masses are determined hereby m Q . Meanwhile, the fine-tuning (the y-axis scale) and the radiative contribution to the Higgsmass are driven by the heavier stop, determined here by m u . The difference between this figure andFig. 14 highlights why naturalness prefers the situation where both stops are roughly degenerate. limits are on the light squarks, the obvious way to reduce fine-tuning is to consider spectrawith a flavor non-degenerate squark soft mass, so that the stops are lighter than the squarksof the first two generations. This scenario has been the focus of our limit study in Sect. IV.However, as pointed out in Sect. III, the flavor degenerate case for the squarks may not bestrongly disfavored yet, due to the dependence of the LHC constraints on the LSP mass.Therefore, it is also interesting to consider flavor degenerate squarks (which are predicted bymany of the simplest scenarios of SUSY breaking, such as gauge mediation), and to checkhow strong the limits really are. This is the subject of the left side of Fig. 16, where weshow the LHC limit coming from the scenario where all squarks are flavor degenerate at theelectroweak scale (including stops and sbottoms), and the gluino mass is fixed to 1.2 TeV,36hich is heavy enough to deplete the rate of associated gluino-squark production. Here wealso made the simplifying choice of taking the Q, U, D soft masses to be equal, althoughmoderate splittings do not drastically change our conclusions.We consider a higgsino LSP and separately scan the common squark mass and the squark-higgsino mass splitting. We see that if the spectrum is mildly compressed, with a squark-higgsino splitting varying from 100-250 GeV, then the limit on the squark masses is in the600 to 700 GeV ballpark range. This limit (and also the 1.2 TeV gluino) corresponds toabout 10% fine-tuning in the Higgs potential, which represents a “best case” scenario for aflavor degenerate boundary condition.It is also likely that the flavor-degenerate option will be more easily constrained by thefuture releases of the LHC data (unless, of course, a signal is found) and may be disfavored inthe next months. If this will be indeed the case, in the context of R-parity conserving naturalSUSY models with MSSM-like signatures, one is naturally led to consider “flavorful” SUSYbreaking scenarios where the third generation squarks is split from the first two generationalready at the SUS mediation scale. The investigation of such models is not new [38] andwas initially motivated by flavor considerations.Not that the flavor non-universal contribution to the squark mass matrices should be atleast of the same order or larger that the flavor-blind one. Generically, if the SUSY mediationmediation mechanism does not commute with flavor, it is likely that additional sources offlavor violation beyond the Minimal Flavor Violation [68] are introduced, as confirmed inexplicit model constructions [69]. These new sources of flavor violation may be detectablein experiments, such as LHCb or a future SuperB factory [70], providing an interestingcomplementarity between direct and indirect searches.However this is not necessarily the case if one can ensure that, even after includingthe SUSY breaking and mediation sectors, the SM Yukawa couplings are the only sourcesof flavor breaking. One possible way to achieve this result could be to couple the SUSYbreaking sector directly to the SSM Higgs sector and hence use the Yukawa couplings totransmit to the squark soft mass matrices a flavorful SUSY breaking contribution, from aninitially flavor-blind SUSY breaking sector [71].We conclude this section with a brief discussion of the limit on gaugino unification. Recallthat throughout this paper, we have decoupled the superpartners whose masses are incon-37
00 400 500 600 700 800 900100150200250300350400 m q (cid:142) (cid:64) GeV (cid:68) m q (cid:142) (cid:45) m H (cid:142) (cid:64) G e V (cid:68) Flavor Degenerate Squarks m g (cid:142) (cid:61) ATLAS 2 (cid:45) (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS M T2 , 1.1 fb (cid:45) CMS Α T , 1.14 fb (cid:45)
400 600 800 1000 1200200300400500600700800 m g (cid:142) (cid:64) GeV (cid:68) m t i (cid:142) (cid:64) G e V (cid:68) Gaugino Unification M : M : M (cid:61) (cid:45) CMS H T (cid:144) MET, 1.1 fb (cid:45) CMS M T2 , 1.1 fb (cid:45) ATLAS 1l, 1.04 fb (cid:45) FIG. 16: On the left we show the limit when the squarks have flavor universal masses and thehiggsino is the LSP. We have fixed the gluino mass to 1.2 TeV and we vary the common squarkmass and the mass splitting between the squarks and the higgsino. We see that if the spectrum iscompressed, the squarks can be as light as 600 GeV, with the strongest limit coming from searchesfor jets and missing energy. This represents a sort of “best case scenario” for flavor degeneracybecause the fine-tuning (both in the compression and the electroweak symmetry breaking) is onlymoderate. On the right we show the limit on gluino versus stop mass, imposing gaugino unification, M : M : M ≈ sequential for naturalness, including the bino and the wino. But it is also interesting torelax this assumption and consider spectra where both the bino and wino are light, becausemany models of supersymmetry breaking, with gauge coupling unification, predict that thegaugino masses appear in the ratio M : M : M ≈ For brevity we do not explicitly consider other gaugino mass relations, such as the anomaly-mediated one, M : M : M ≈ . VI. CONCLUSIONS
We have investigated the current LHC limits on Natural SUSY, i.e. on supersymmetricscenarios where the higgsinos, the top squarks, the left-handed bottom squark, and the gluinoare bound to be light from the requirement of natural electroweak symmetry breaking. Wefound that the most constraining searches are those looking for the jets+ /E T signatures inthe case of stops and sbottom decaying to neutralinos and charginos, while a combinationof jets+ /E T and same-sign (SS) dilepton searches for the cascades initiated by the gluino.Our main results are summarized in in Tables II and III, where we show the mass limitsfound for the various simplified models studied, together with a reference to the relevantplot in this paper. The luminosity of 1 f b − marks a divide in the LHC SUSY searches,after which it is possible to start looking in detail for direct production of third generationsquarks, complementing the searches already looking for them in processes initiated by gluinopair production. With higher luminosities it will also be possible to probe direct higgsinoproduction, which will be another necessary step towards probing the natural region ofSUSY.On one hand we find that the current searches already started probing the direct pro- that those presented here.
00 300 400 500 600100150200250300350400 m t L (cid:142) (cid:64) GeV (cid:68) m H (cid:142) (cid:64) G e V (cid:68) Left (cid:45)
Handed Stop (cid:144)
Sbottom
CMS H T (cid:144) MET, 10 fb (cid:45) CMS M T2 , 10 fb (cid:45) ATLAS jets (cid:43)
MET, 10 fb (cid:45) (cid:45) m b L (cid:142) (cid:61) m H (cid:142)
200 300 400 500 600100150200250300350400 m t L (cid:142) (cid:64) GeV (cid:68) m H (cid:142) (cid:64) G e V (cid:68) Right (cid:45)
Handed Stop
CMS H T (cid:144) MET, 10 fb (cid:45) CMS M T2 , 10 fb (cid:45) ATLAS jets (cid:43)
MET, 10 fb (cid:45) (cid:45) m t R (cid:142) (cid:61) m H (cid:142) FIG. 17: The estimated 95% exclusion reach, with 10 fb − , for left-handed stop/sbottom ( left ) andright-handed stop ( right ), with higgsino LSP. We show the reach by extrapolating the cuts of theexisting searches for jets and missing energy. We find that the reach is highly sensitive to the treat-ment of systematic errors. For the solid curves, we assume that statistical errors will reduce withluminosity but that systematic errors will remain a constant fraction of the background estimate.For the dashed curves, we take the idealized limit of zero statistical or systematic uncertaintieson the background estimate, taking the central value of the backgrounds reported in the currentexperimental searches. duction of third generation squarks, mostly in the b + χ decay channel. On the other hand,we find similar bounds on gluinos decaying through third generation squarks as those foundby the experimental collaborations, but with the striking feature that tailored searches forgluinos decaying into heavy flavor squarks are currently not providing the most stringentbounds.We do not attempt to make any future projections for the mass reach for stops, bottoms,higgsinos and the gluino for 5 and 10 f b − of LHC data. The main reason is that the largestgain in reach will be likely come from new analyses designed and optimized for the parameterspace regions where the current analyses are less powerful. Designing such analyses is beyond40
00 600 800 1000 1200 1400300400500600700800900 m g (cid:142) (cid:64) GeV (cid:68) m t i (cid:142) (cid:64) G e V (cid:68) Higgsino LSP w (cid:144)
10 fb (cid:45) CMS Α T CMS M T2 CMS H T (cid:144) MET (cid:45) FIG. 18: The estimated 95% exclusion reach, with 10 fb − , for the higgsino LSP benchmark. Asin Fig. V, the solid lines extrapolate the current systematic and statistical errors on the background,while the dashed lines assume perfect knowledge of the background. The large spread between theseestimates emphasizes the importance of the eventual systematic errors for the reach.production LSP ˜ t limit [GeV] figure˜ t L + ˜ b L ˜ H ∼
250 3˜ t R ˜ H ∼
180 3˜ t L + ˜ b L ˜ B ∼ −
350 5TABLE II: A summary of the limits we found on direct stop and left-handed sbottom productionwith higgsino and bino LSPs. The full limits are shown in the listed figures and the parameterspaces are described in the text of section IV B. the scope of this work, and it requires a detailed study of the backgrounds, some of which,such as fakes, cannot be reliably estimated in a theoretical paper. Moreover, even the pureextrapolation of the reach of the current searches is plagued by intrinsic difficulties, not41 cenario ˜ g limit [GeV] ˜ t limit [GeV] figure˜ H - LSP ∼ − ∼
280 10˜ B - LSP ∼ ∼
270 10somewhat squashed ∼ − − t ∼ − − −
900 16gaugino unify ∼ − ∼
260 16TABLE III: A summary of limits that we found in scenarios with gluinos. The full limits are shownin the listed figures and the parameter spaces are described in the text of sections IV C and V. unrelated to those relevant for designing new analyses, which are discussed in Appendix C.We conclude by observing that the experimental program of searches for supersymme-try is crossing an important milestone. The current searches are passing the naturalnessthreshold for stops and gluinos, and this means that the most favored parameter space ofsupersymmetry is just ahead of us. If supersymmetry exists at the weak scale in a naturalform, then discovery should be imminent. On the other hand, if the LHC experiments fail todiscover supersymmetry in the natural parameter space then, as the fine-tuning is increased,exotic manifestations of supersymmetry that are less constrained, such as hadronic R -parityviolation [72] or stealth SUSY [66], will become increasingly more interesting alternatives,both theoretically and experimentally. The next frontier may be heavy-flavor-themed nat-uralness, or exotic searches. Either way, the LHC will cover very exciting ground over thecoming years. Note added : While this work was being completed, the authors of [73–75] informed usabout related but distinct collider studies involving third generation squarks.
Acknowledgments
We acknowledge P. Schuster and N. Toro for participation at an early stage of thiswork. We thank M. R. d’Alfonso, J.-F. Arguin, S. Caron, B. Heinemann, A. Hoecker,42. A. Koay, M. d’Onofrio, S. Padhi, M. Pierini, P. Pralavorio, G. Redlinger, C. Rogan,R. Rossin, M. Spiropulu, and I. Vivarelli for many suggestions and patiently answering ourquestions about the ATLAS and CMS searches. We also thank N. Arkani-Hamed, R. Barbi-eri, C. Cheung, S. Dimopoulos, G. F. Giudice, L. J. Hall, I. Low, M. Perelstein, G. Weigleinand N. Weiner for discussions. M.P. and A.W. thank E. Gianolio for computing support.J.T.R. thanks the Institute for Advanced Study for kindly providing access to the AuroraCluster. The work of M.P. was supported in part by the US Department of Energy underContract DE-AC02-05CH11231. J.T.R. is supported by a fellowship from the Miller Insti-tute for Basic Research in Science. M.P. and J.T.R. would like to thank the Aspen Centerfor Physics where part of this work was conducted. The work of A.W. was supported in partby the German Science Foundation (DFG) under the Collaborative Research Center (SFB)676.
Appendix A: Validation of the analyses implementations
In order to check whether our PGS/Atom implementations are giving results in reasonableagreement with those obtained by the experimental collaborations, for each analyses wevalidated them by comparing with the publicly available data. There are two kind of plotsthat one can compare the results to: kinematic distributions and exclusion limits.In the first case the event distribution for a particular observable is plotted for a specificsignal model and a specific point in parameter space. Comparing against such a histogram isvery useful to detect kinematic distortions induced by our approximations (from the shapeof the distribution) and to compare precisely the signal acceptances and efficiencies, (cid:15) × A (from the histogram normalization). Examples of such comparisons are shown in Fig. Afor two different cases: the /E T significance for the ATLAS 6-8 jets+ /E T search and the α T distribution for the CMS search. As one can see both of our pipelines reproduce reasonablywell the kinematic distributions and acceptances of hadronic SUSY searches without theneed of further adjustments, which is important since many of our limits depend on jets+ /E T analyses.One drawback is that the comparison is for a specific point in parameter space, thereforeone cannot detect potential problems in different kinematical regions. A different cross-check43 (cid:45)
110 MET (cid:144) H T (cid:64) GeV (cid:144) (cid:68) E v e n t s (cid:144) . G e V (cid:144) ATLAS 6 (cid:45)
ATLASATOMPGSL (cid:61) (cid:45) Α T E v e n t s (cid:144) . CMS Α T Validation
CMSATOMPGS L (cid:61) (cid:45) FIG. 19: Validation of kinematic plots for ATOM and PGS. The left plot shows the missing energysignificance in the ATLAS 6-8 jets plus missing energy search, for the MSUGRA benchmark pointwith m = 1220 GeV and m / = 180 GeV, tan β = 10, and A = 0 GeV. The right plot showsthe distribution of α T for the CMS search using this variable and the MSUGRA benchmark pointLM6. In both plots, the signal region is to the right of the vertical black dashed line, and we findgood agreement between the experimental simulations, and ATOM and PGS. is instead provided by exclusion plots, such as the simplified models or the classic limit inthe CMSSM plane. In many cases these are the only plots one can compare to. Here thecurves represent mass limits, which are often easier to match given that the steeply fallingcross-section tend to reduce the effects of a discrepancy in (cid:15) × A . On the other hand suchcomparisons have the ability to check the agreement of our implementations in differentkinematical regions at once. However other sources of disagreement may appear and theyrender the process of debugging discrepancies considerably harder. A typical example is theeffect of including systematic uncertainties on the signal in order to produce the limit, whichtypically introduce an intrinsic uncertainty in the comparison due to lack of information.In Fig. A one can see the results for two of such comparisons, the mSUGRA limit for theSame-Sign dilepton CMS search and the ATLAS bjets+0leptons+ /E T analysis. In particularthe latter analysis also shows the stronger level of discrepancy (a factor of 2 in (cid:15) × A ) amongall our comparisons, most likely due to systematics on the signal we did not include. Howeverwe did check, by using a crude estimate of their size from [3], that the CL s limits on event44
10 Summary and Conclusions
As a reference to other searches for SUSY, we interpret results in search region 1 in the context ofCMSSM model. The observed upper limits on the number of signal events reported in Section 8are compared to the expected number of events in the CMSSM model in a plane of ( m , m ) for tan β = A =
0, and µ >
0. All points with mean expected values above this upperlimit are interpreted as excluded at the 95% CL. The observed exclusion region for the high-p T dilepton selection is displayed in Fig. 5. The shaded region represents the uncertainty on theposition of the limit due to an uncertainty on the production cross section of CMSSM resultingfrom PDF uncertainties and the NLO cross section uncertainty estimated from varying therenormalization scale by a factor of two. The expected exclusion region is approximately thesame as the observed one. An exclusion region based on our previous analysis [9] is also shownfor a comparison. The new result extends to gluino masses of 825 GeV in the region with similarvalues of squark masses and extends to gluino masses of 675 GeV for higher squark masses.This can be compared to the exclusion of just around 500 GeV in the previous analysis. Theresult for the inclusive dilepton selection is also shown in Fig. 6. (GeV) m ( G e V ) / m (500)GeVq~ (500)GeV g~ (750)GeVq~ (750)GeV g~ (1000)GeVq~ (1000)GeV g~ (1250)GeVq~ (1250)GeV g~ = 7 TeVs, -1 = 0.98 fb int CMS Preliminary, L ) > 0 µ = 0, sign( = 10, A ! tan ± " LEP2 ± l~ LEP2 = LSP $ NLO Observed LimitNLO Expected Limit ) -1 = 35 pb int NLO Observed Limit (2010, L
Figure 5: Exclusion region in the CMSSM corresponding to the observed upper limit of 3.0events in the search region 1 of the high-p T dilepton selections. The result of the previous analy-sis [9] is shown to illustrate the improvement since.
10 Summary and Conclusions
We have searched for new physics with same-sign dilepton events in the ee, µµ , e µ , e τ , µτ , and ττ final states, and have seen no evidence for an excess over the background prediction. The τ leptons referred to here are reconstructed via their hadronic decays. PGSATOM [GeV] g~ m
100 200 300 400 500 600 700 800 900 1000 [ G e V ] b ~ m !" b+ b~ production, b~- b~ + g~-g~ =7 TeVs, -1 L dt = 0.83 fb $ b-jet analyses0 lepton, 3 jets Preliminary
ATLAS q~) = 60 GeV, m( !" m( b f o r b i d d e nb ~ g ~ observed limit s CL expected limit s CL68% and 99% C.L. expected limits s CL ) -1 ATLAS (35 pb -1 b~ b~CDF -1 b~ b~D0 -1 b 2.5 fb b~ , g~g~CDF Figure 4: Observed and expected 95% C.L. exclusion limits in the ( m ˜ g , m ˜ b ) plane. Also shownare the 68% and 99% C.L. expected exclusion curves. For each point in the plot, the signal regionselection providing the best expected limit is chosen. The neutralino mass is set to 60 GeV. Theresult is compared to previous results from ATLAS and CDF searches which assume the samegluino-sbottom decays hypotheses. Exclusion limits from the CDF and D0 experiments ondirect sbottom pair production are also shown.are heavier than the gluino, which decays exclusively into three-body final states ( b ¯ b ˜ ! ) viaan off-shell sbottom. Such a scenario can be considered complementary to the previous one.The exclusion limits obtained on the ( m ˜ g , m ˜ ! ) plane are shown in Figure 5 for gluino massesabove 200 GeV. For each combination of masses, the analysis providing the best expected limitis chosen. The selection 3JD leads to the best sensitivity for gluino masses above 400 GeVand % M ( ˜ g − ˜ ! ) > GeV. At low % M ( ˜ g − ˜ ! ) , soft b -jets spectra and low E missT are expected,giving higher sensitivity to the signal regions 3JA and 3JB are preferred. Low gluino massscenarios present moderate m eff and high b -jet multiplicity, thus favouring signal region 3JC.Neutralino masses below 200-250 GeV are excluded for gluino masses in the range 200-660 GeV,if % M ( ˜ g − ˜ ! ) >
100 GeV.The results can be generalised in terms of 95% C.L. upper cross section limits for gluino-like pair production processes with produced particles decaying into b ¯ b ˜ ! final states. Thecross section upper limits versus the gluino and neutralino mass are also given in Figure 5.The results are finally employed to extract limits on the gluino mass in the two SO(10)scenarios, DR3 and HS. Gluino masses below 570 GeV are excluded for the DR3 model. In thiscase ˜ g → b ¯ b ˜ ! decays dominate up to gluino masses of 550 GeV: above this range, high BR fordifferent decay modes decrease the sensitivity of the selected final states. A lower sensitivity, m ˜ g < GeV, is found for the HS model, where larger branching ratios of ˜ g → b ¯ b ˜ ! are expectedand the efficiency of the selection is reduced with respect to the DR3 case ( m ˜ ! ≈ × m ˜ ! ). An update on the search for supersymmetry in final states with missing transverse momen-tum, b -jet candidates and no isolated leptons in proton-proton collisions at 7 TeV is presented.The results are based on data corresponding to an integrated luminosity of 0.83 fb − collected9 PGSATOM
FIG. 20: Validation of exclusion limit plots for ATOM and PGS. The left plot shows the CMSSMlimit for the Same-Sign dilepton search by CMS, and superimposed the PGS (green) and ATOM(brown) curves. The dashed curve represent the PGS prediction before correcting for the differencein lepton identification efficiencies between the code (90%) and the CMS analysis (roughly 70%),while the solid line correspond to the final result. The right plot shows instead the exclusion limit forthe gluino-sbottom-neutralino simplified model presented in the b-jets+0 (cid:96) + /E T ATLAS analyses.PGS (ATOM) curves are shown in green (brown), where the dashed line is the limit before thefactor of 2 correction on the event yield due to the systematic uncertainties on the signal, and thesolid line is the final result. yields may vary by a factor of two. Therefore we decided to apply this correction factoreverywhere in our study. Fig. A shows the effects of this rescaling.
Appendix B: Brief description of “ATOM”
ATOM (“Automatic Test Of Models”) is the tentative name of a tool currently developedby some of the authors and it is intended to be released in the future for the free use to thecommunity. The purpose of such tool is to provide, by running locally on the user’s com-45uter, a relatively fast approximate (although often “good enough”) answer to the questionwhether a specific model is excluded or not by a set of experimental searches. It does notaim to provide the full correct answer, which can be provided only by a real study by theexperimental collaborations or by more powerful tools like RECAST [76] currently underdevelopment. A detailed description of the package will be given elsewhere [40], here wewill just highlight the main features. The tool accepts particle events as a definition for themodel currently being tested. The event processing is performed by the Rivet package [77]upon which ATOM is built. An advantage of Rivet is that a large number of analyses canbe performed simultaneously without a significant extra cost in CPU time. As in the baseversion of Rivet, ATOM processes the input events through the cuts of the implementedanalyses and populates the various histograms present in the various experimental papers.For the analyses we have coded, we included also the various plots corresponding to thecontrol regions used by the analyses to determine the backgrounds. This is important in orderto check whether a new physics signal may substantially leak into a control region for a searchand be “subtracted away”, especially if the latter has not been specifically designed for thatparticular model. Differently than the base version of Rivet, ATOM automatically savesthe information about signal efficiencies at various stages of the analyses, both for the totalsignal events and for each individual sub-process. Moreover, for each cut, it automaticallycomputes the sensitivity of the signal efficiency to the precise value of that cut (defined asthe logarithmic derivative of the efficiency with respect to the cut position). We use thisfeature to detect regions where the cuts are applied on steeply falling signal distributions,leading to large uncertainties in the final efficiency as, e.g. , in Fig. 10.All this additional information in addition to the Rivet histograms is parsed by ATOMto flag potential problems for the results of the analyses with the signal events at hand. Thefinal efficiencies are then used in the statistics module to extract the exclusion limits.The events are processed by default at truth level as in Rivet. Jets are clustered withFastJet [78]. We perform lepton isolation at particle level according to the parametersspecified in the experimental papers and we reconstruct b-jets by determining whether theparticles clustered in a jet have a b-quark ancestor and then applying a tagging efficiency asspecified by the searches.We have implemented in ATOM also the possibility to use parameterised efficiency spec-46fied as 2D histograms in p T and η for all the various objects, as well as the possibility ofincluding smearing. However we do not use them in the present study and we limit ourselvesto apply the reconstruction efficiency for leptons as a constant correction factors wheneverspecified in the papers. Appendix C: Projections for the current analyses
400 600 800 1000 1200 1400300400500600700800900 m g (cid:142) (cid:64) GeV (cid:68) m t i (cid:142) (cid:64) G e V (cid:68) Higgsino LSP w (cid:144)
10 fb (cid:45) CMS Α T CMS M T2 CMS H T (cid:144) MET (cid:45) FIG. 21: Possible range for the projections of the current analyses to 10 f b − of LHC data in thecase of gluinos and stops decaying to higgsino LSP. The solid lines correspond to the conservativeassumption of rescaling the statistical errors with the luminosity and keeping the relative systematicas constant, while the dashed lines correspond to the extremely optimistic case of perfect knowledgeof the backgrounds. Here we discuss the (im)possibility of extrapolating to higher luminosities the reach of thecurrent analyses, given the limitations of our “theorist” analysis. The most naive (and con-servative) extrapolation would be to scale the statistical errors with the increased luminosityand keep the relative systematic error as constant. However one notices immediately that inmost of the analyses the systematic errors on the backgrounds are of the same order as the47tatistical ones. Therefore even with a large increase in luminosity the limit on the cross-section would improve only by a factor of ∼ √
2, which corresponds to a limited increase inthe mass reach. This is unlikely to be the case, the reason being that in most of the casesthe systematic errors have been currently reduced to be a subdominant component of theerror budget, even if there may still be the possibility of further improvements. The correctprocedure would be to study in detail the systematic error budget and estimate for each ofthem what would be the improvement in the future, a task clearly beyond the scope of thispaper. On the other extreme, one could try to understand what would be the upper limit onthe improvement by (unrealistically) assuming a perfect knowledge of the background andinclude only the Poissonian error in computing the limits. Obviously the correct answer liesin between these two extrema, but as one can see from Fig. 21 the mass range spanned bythese two limits is extremely large, rendering useless any projections done with our means.There is another reason for avoiding any attempt for giving projections: in many cases thebackgrounds in the signal regions are determined by control regions and therefore are sensi-tive to statistical fluctuations there in the current dataset. This is the case, e.g. , for the CMS M T analyses where, as stated in [13] a downward fluctuation in the last bin of the controlregion, have determined a lower background estimate in the signal region. Extrapolating theprojections to 10 f b − would yield very powerful constraints as shown in Fig. 21, that wouldbe completely overestimated if indeed the low background is due to a statistical fluctuation. [1] ATLAS Collaboration, “Search for squarks and gluinos using final states with jets and missingtransverse momentum with the ATLAS detector in sqrt(s) = 7 TeV proton-proton collisions,”arXiv:1109.6572 [hep-ex].[2] ATLAS Collaboration, “Search for new phenomena in final states with large jet multiplicitiesand missing transverse momentum using √ s = 7 TeV pp collisions with the ATLAS detector,”arXiv:1110.2299 [hep-ex].[3] ATLAS Collaboration, “Search for supersymmetry in pp collisions at √ s = 7 TeV in finalstates with missing transverse momentum, b-jets and no leptons with the ATLAS detector,”ATLAS-CONF-2011-098, July 2011.
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