Search for a compressed supersymmetric spectrum with a light gravitino

Journal of High Energy Physics, Sep 2017

Presence of the light gravitino as dark matter candidate in a supersymmetric (SUSY) model opens up interesting collider signatures consisting of one or more hard photons together with multiple jets and missing transverse energy from the cascade decay. We investigate such signals at the 13 TeV LHC in presence of compressed SUSY spectra, consistent with the Higgs mass as well as collider and dark matter constraints. We analyse and compare the discovery potential in different benchmark scenarios consisting of both compressed and uncompressed SUSY spectra, considering different levels of compression and intermediate decay modes. Our conclusion is that compressed spectra upto 2.5 TeV are likely to be probed even before the high luminosity run of LHC. Kinematic variables are also suggested, which offer distinction between compressed and uncompressed spectra yielding similar event rates for photons + multi-jets + .

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Search for a compressed supersymmetric spectrum with a light gravitino

Revised: July Search for a compressed supersymmetric spectrum Juhi Dutta 0 1 Partha Konar 0 1 Subhadeep Mondal 0 1 Biswarup Mukhopadhyaya 0 1 Santosh Kumar Rai 0 1 Harish-Chandra Research Institute, HBNI, 0 Ahmedabad 380009 , India 1 Chhatnag Road, Jhusi , Allahabad 211019 , India Presence of the light gravitino as dark matter candidate in a supersymmetric (SUSY) model opens up interesting collider signatures consisting of one or more hard photons together with multiple jets and missing transverse energy from the cascade decay. We investigate such signals at the 13 TeV LHC in presence of compressed SUSY spectra, consistent with the Higgs mass as well as collider and dark matter constraints. We analyse and compare the discovery potential in di erent benchmark scenarios consisting of both compressed and uncompressed SUSY spectra, considering di erent levels of compression and intermediate decay modes. Our conclusion is that compressed spectra upto 2.5 TeV are likely to be probed even before the high luminosity run of LHC. Kinematic variables are also suggested, which o er distinction between compressed and uncompressed spectra yielding similar event rates for photons + multi-jets + E=T . Supersymmetry Phenomenology 1 Introduction 2 Compressed spectrum with a gravitino LSP 2.1 Relevant branching ratios 2.1.1 2.1.2 2.1.3 Summary and conclusion Simulation set up and analysis Distinction of compressed and uncompressed spectra interacting sparticles are still not that severely constrained [7, 8]. With the LHC already operating close to its near maximum centre-of-mass energy, consistent improvements in luminosity is expected to help accumulate enough data which will help probe the coloured sector mass to almost 3 TeV with some improvements for the weakly interacting sector too. This lack of evidence for any low scale SUSY events prompted the idea of a compressed sparticle spectrum [9{21], where the lightest SUSY particle (LSP) and the heavier sparticle states may be nearly degenerate. In such realizations of the mass spectra, the resulting nal state jets and leptons from the decay cascades of the parent particles are expected cascades. Usually, in most SUSY models, the lightest neutralino ( e01) is assumed to be the LSP. Thus, such signals allow a much lighter SUSY spectrum compared to the conventional channels with hard leptons, jets and large missing transverse momentum [22{32]. However, in the presence of a light gravitino (Ge) in the spectrum, such as in gauge mediated SUSY breaking (GMSB) models [33{40], the e01 is quite often the next-to-lightest SUSY particle (NLSP), which decays into a Ge and a gauge/Higgs boson. Search strategy for such scenarios, therefore, is expected to be signi cantly di erent. In this case, one would always expect to nd one or more hard leptons/jets/photons in the nal state originating from the Hence detecting events characterizing such a signal is expected to be much easier, with e01 decay, irrespective of whether the SUSY mass spectrum is compressed or not. the preferred channel being the photon mode. Given the fact that the hard photon(s) can easily be tagged for these events in a relatively compressed spectrum of the SUSY particles with the NLSP, one need not rely on the radiated jets for signal identi cation, thereby improving the cut e ciency signi cantly. If one considers a xed gravitino mass, the photon(s) originating from the e01 decay will be harder as me01 becomes heavier. Hence these hard photon associated signals can be very e ective to probe a heavy SUSY spectrum with a light gravitino as there would rarely be any SM events with such hard photons in the nal state. While the light gravitino scenario yields large transverse missing energy (E=T ) as well as hard photon(s) and jet(s), the question remains as to whether its presence obliterate the information on whether the MSSM part of the spectrum is compressed or not. In this work, we have demonstrated how such information can be extracted. Our study in this direction contains the following new observations: A set of kinematic observables are identi ed involving hardness of the photon(s), the transverse momenta (pT ) of the leading jets and also the E=T , which clearly brings out the distinction between a compressed and an uncompressed spectrum with similar signal rates. We have studied di erent benchmarks with varied degree of compression in the spectrum in this context. The characteristic rates of the n- (where n 1) nal state in a compressed spectrum scenario have been obtained and the underlying physics has been discussed. The circumstances under which, for example, a gluino in a compressed MSSM spectrum prefers to decay into a gluon and a gravitino rather than into jets and a neutralino have been identi ed. In this context, we have also found some remarkable e ects of a eV-scale gravitino though such a particle can not explain the cold dark matter (DM) content of the universe. { 2 { bounds on the coloured sparticles [41{48]. The ATLAS collaboration recently published their analysis on a SUSY scenario with a light Ge with the 13 TeV data accumulated at an integrated luminosity of 13:3 fb 1 [48]. In this analysis, e01 is considered to be a binohiggsino mixed state decaying into Ge and(or) ZGe resulting in the nal state \n1 + n2 jets + E=T " where n1 1 and n2 > 2. The 13 TeV data puts a stringent constraint on the sparticle masses excluding mg upto 1950 GeV subject to the lightest neutralino mass close to 1800 GeV [46{48], which ies a signi cant improvement on the bounds obtained after the 8 TeV run with 20:3 fb 1 integrated luminosity [42, 44]. We note that, in order to derive the limits from the collider data, the experimental collaboration considers signal events coming from gluino pair production only, while assuming the rest of the coloured sparticles viz. squarks to be much heavier to contribute to the signal. The robustness of the signal however does not di erentiate whether such a heavy SUSY spectrum (leaving aside the gravitino) are closely spaced in mass or have a widely split mass spectrum, and whether it is just a single sparticle state that contributes to the signal or otherwise. We intend to impress through this work that such a signal would also be able to distinguish such alternate possibilities quite e ciently. In an earlier work while assuming a similar compression in the sparticle spectrum [18] we had shown that in order to get a truly compressed1 pMSSM spectrum consistent with a 125 GeV Higgs boson and the avour and dark matter (DM) constraints, one has to have the e10 mass at or above 2 TeV with the entire coloured sector lying slightly above. Such a spectrum is now seemingly of interest given the present experimental bounds obtained in Ge LSP scenario.2 In this work, we aim to extend our previous study by adding to the spectrum, a Ge LSP with mass, at most, in the eV-keV range. Rest of the pMSSM spectrum lies above the TeV range to be consistent with the experimental bounds. This is in contrast to existing studies done earlier for gravitino LSP which we compare by studying the prospects of uncompressed spectra having relatively larger mass gaps between the coloured sparticles and e10, but with event rates similar to that of the compressed spectra. Since the kinematics of the decay products in the two cases are expected to be signi cantly di erent, we present some kinematical variables which clearly distinguish a compressed spectrum from an uncompressed one, in spite of comparable signal rates in both cases. The paper is organised in the following way. In section 2 we discuss about the phenomenological aspects of a SUSY spectrum with gravitino LSP and then move on to study the variation of the branching ratios of squark, gluino and the lightest neutralino into gravitino associated and other relevant decay modes. In section 3 we present some sample benchmark points representative of our region of interest consisting of both compressed and uncompressed spectra that are consistent with the existing constraints. Subsequently, in section 4 we proceed to our collider analysis with these benchmark points and present the details of our simulation and obtained results. Finally, in section 5 we summarise our results and conclude. 1Mass gap between the heaviest coloured sparticle and the LSP neutralino has to be around 100 GeV. 2Note that the bounds on the squark-gluino masses in the compressed region with e 01 LSP are still much weaker. In such cases, the gluinos and rst two generation squarks are excluded upto 650 GeV and 450 GeV respectively [30]. { 3 { The NLSP decaying into a gravitino and jets/leptons/photons give rise to very distinct signals at the LHC. Both the ATLAS and CMS collaborations have studied these signal regions for a hint of GMSB-like scenarios [41{48]. Note that, a pure GMSB like scenario is now under tension after the discovery of the 125 GeV Higgs boson [49{51]. It is very di cult to t a light Higgs boson within this minimal framework, mostly because of small mixing in the scalar sector. As a consequence, the stop masses need to be pushed to several TeV in order to obtain the correct Higgs mass, thus rendering such scenarios uninteresting in the context of LHC. However, some variations of the pure GMSB scenario are capable of solving the Higgs mass issue and can still give visible signals within the LHC energy range [52, 53]. Since we are only interested in the phenomenology of these models here, a detailed discussion on their theoretical aspects is beyond the scope of this paper. Although the lightest neutralino ( e01) is the more popular DM candidate in SUSY theories, gravitino (Ge) as the LSP has its own distinct phenomenology. The Ge is directly related to the e ect of SUSY breaking via gauge mediation and all its couplings are inversely proportional to the Planck mass ( 1018 GeV) and thus considerably suppressed. The hierarchy of the sparticle masses depend on the SUSY breaking mechanism and can result in Ge getting mass which is heavier, comparable or lighter than the other superpartners. Thus if it happens to be the LSP in the theory, Ge can also be a good DM candidate [54{59] making such scenarios of considerable interest in the context of the LHC. In addition, having Ge as a DM candidate also relaxes the DM constraints on the rest of the SUSY spectrum by a great deal, allowing them to be very heavy while being consistent with a light Ge DM. However, a very light Ge is mostly considered to be warm DM. Present cosmological observations require a light gravitino to have a mass close to a few keV [60, 61] at least, if it has to explain the cold DM relic density. However, the kinematic characteristics of events when the NLSP decays into a gravitino are mostly independent of whether the gravitino is in the keV range or even lower in mass. Some special situations where the di erence is of some consequence have been discussed in section 4.3. Of course, the presence of a gravitino much lighter than a keV will require the presence of some additional cold DM candidate. Note that with Ge as the LSP decay branching ratios (BR) of the sparticles can be signi cantly modi ed since they can now decay directly into Ge instead of decaying into e01, which may signi cantly alter their collider signals. The decay width ( ) of a sparticle, scalar(fe) or gaugino(Ve ), decaying into their respective SM counterparts, chiral fermion(f ) or gauge boson(V ), and Ge is given by [62] fe ! f Ge Ve ! V Ge = = 1 48 1 48 m5 f e MP2 lm2G 41 e m5 V e MP2 lm2G e 2 " 1 m m once the sparticles become very heavy and the Ge becomes light. coloured sparticles and their subsequent decays into the Ge via e10, the decay modes of ge, q and e10 are of our primary interest. While considering the decay modes, we focus on e a simpli ed assumption that the decaying coloured sparticle is the next-to-next-lightest supersymmetric particle (NNLSP) with e10 as the NLSP and Ge as the LSP. The BR computation and spectrum generation was done using SPheno [63{65] for a phenomenological MSSM (pMSSM) like scenario with one additional parameter, i.e, the gravitino mass (mG). e 2.1.1 Variation of BR(ge ! gGe) In gure 1 we show the variation of two relevant gluino decay mode channels viz. ge ! gGe and ge ! qq e01 where all the squarks are heavier, as a function of me01 and mG. The gluino mass has been xed to mg=2500 GeV while me01 hamsbgeeee01n=vamrigeed such that e likme.geeI01n vtahreieasbwseitnhcien o1f0-it1s50tw0Go-ebVod.yNdoteecaetyhamt otdhee ien01toisscqounasrikd-eqruedartkopbaeirds,omthienagnlutliynobicnaononly decay via ge ! gGe or ge ! qq e01. The other two-body decay mode ge ! g e01 being loop suppressed, remains mostly subdominant compared to these two decay modes. Hence, only the two relevant channels are shown in the gure. Note that, BR(ge ! qq e01) includes the sum of all the o -shell contributions obtained from the rst two generation squarks which in this case lie about 100 GeV above mg. As the gravitino mass gets heavier, BR(ge ! gGe) decreases since, the corresponding partieal width is proportional to the inverse square of m . Similarly, as me01 keeps increasing, BR(ge ! qq e01) goes on decreasing. Note that, the BR for the 3-body decay mode can decrease further with increase in the corresponding squark masses. However, even for a keV Ge, BR(ge ! gGe) can remain signi cantly large provided there is su cient compression in the mass gap ( mgee01 10 GeV) as seen in gure 1. { 5 { ! qGe) and BR(qeL=R ! q e01) in the plane e plots on the left show the distributions corresponding to the up-squarks and the ploetes1 on the right mq 0 - mG. The show the same for the down-squarks. 2.1.2 Variation of BR(qeL=R ! qGe) Next we look into the relevant decay modes of the rst two generation squarks3 when they are the NNLSP's. In this case, we assume that the gluino is heavier than the squarks, and qeL=R ! q e01 so that the dominant two-body decay modes available to the squarks are qeL=R ! qGe . Unlike the previous case, here the gravitino decay branching ratio has competition from another two-body decay mode. Although the decay into Ge does not depend on the L and R-type of the squarks, BR(qeL=R ! q e01) is expected to be di erent 0 depending on the composition of the e1 . For simplicity, we choose the e10 to be purely bino-like as before. The squark masses are xed at mq = 2500 GeV and the NLSP mass, me01 is varied as before such that The branching probabilities are shomwnqeei01n= mq guree 2 where the plots on the left (right) shows me01 vearies in a wide range, 10-1500 GeV. and bino-component of e10 is proportional to p2g tan W (I3q the decay branching ratios of uL=R (dL=R). As the coupling of qeL with the SM-quark eq) while that of qeR is 3Since the production cross-section of the third generation squarks are substantially smaller than those of the rst two generations, we do not consider the production of the stop and sbottom states. Hence we only discuss the decays of u~L=R and d~L=R. { 6 { proportional to p2g tan W eq, where g; eq and I3q represents SU(2) gauge coupling, electric charge of the SM-quark and its isospin respectively [62], we nd a noticeable variation in decay probabilities of qeL and qeR for the same choice of mass spectrum. This implies that the right-handed squarks couple more strongly with the e10 compared to the lefthanded ones. As a result, although the partial decay widths of the squarks decaying into gravitino and quarks are identical for squarks of similar mass, the corresponding BR vary obtained similar distributions corresponding to those. slightly depending on their handedness. This feature is evident in gure 2. The coupling strength of uR with e10 is larger by a factor of four compared to that of ueL. The same e coupling corresponding to deR is larger by a factor of two compared to that of deL. Hence the di erence in the BR distributions is more manifest for the up-type squarks. The magnitude of the coupling strengths corresponding to uL and deL are exactly same and hence we have e The BR distributions indicate that as we go on compressing the SUSY spectrum, the gravitino decay mode becomes more and more relevant but only if its mass is around or below the eV range. We, therefore, conclude that for a keV Ge, the decay mode ge ! gGe may be of importance but only for the cases where the gluino mass lies very close to the NLSP very small and the decay of the squarks into neutralino mass. For the rst two generation squarks and a keV Ge, the BR(qeL=R ! qGe) is e01 dominates in the absence of a lighter gluino. As evident, the gravitino decay mode can be of signi cance for LHC studies if m eV. However, such a light Ge is strongly disfavoured from DM constraints as mentioned before. G e 2.1.3 Variation of BR( e01 ! XGe) The last two subsections point out the situations where the NLSP can be bypassed in the decay of strongly interacting superparticles. Such events tend to reduce the multiplicity of hard photons in SUSY-driven nal states. In contrast, in the case where the SUSY cascades lead to a e10 NLSP, the e10 may further decay into gravitino along with a Z, or the Higgs boson (h) depending upon its composition.4 The h-associated decay width is entirely dependent on the higgsino component of on the bino and wino component of e01 whereas the Z-associated decay width has a partial 0 dependence on all the components that make up the e1 the di erent composition strengths of e01 in its decay width can be summarised as [62]: . The functional dependence on e01 while ( e01 ! Ge) depends entirely 0 e1 ! 0 e1 ! ZGe 0 e1 ! hGe G e / jN11cos W + N12sin W j 2 / jN11sin W / jN14sin N13cos j2 1 2 N12cos W j2 + jN14cos N13sin j2 (2.3) (2.4) (2.5) where, Nij are the elements of the neutralino mixing matrix, W is the Weinberg mixing angle, is the neutral Higgs mixing angle and corresponds to the ratio of the up and down type Higgs vacuum expectation values (VEVs). Note that the partial decay widths e1 are proportional to m5 0 =(MP2 lm2G) and hence if m e G is too large, the total decay width e 4In principle, e10 may decay into the other neutral Higgs states also which we assume to be heavier. { 7 { components. The red, green and blue lines correspond to BR( e01 ! of e01 may become too small such that it will not decay within the detector. Although the decay width is also dependent upon me01 , one nds that for a 2500 GeV e10, and a MeV Ge the neutralino becomes long-lived. In 0 relevant BRs with the composition of the e1 range [2 : 2:5] TeV with the condition gure 3 we show the variation of the three . Here we have varied M1; M2 and in the > M2 > M1 such that e10 is bino-like most of the time with di erent admixtures of wino and higgsino components. The other relevant mixing parameter tan is kept xed at 10. The red, green and blue colours correspond to BR( e01 ! fraction in the composition of e01. Similarly, jN12j2 and jN123j + jN14j2 represent the wino Ge), BR( e01 ! ZGe) and BR( e01 ! hGe) respectively. jN11j2 indicates the binoand higgsino components respectively. As can be clearly seen from the plots, obtaining 100% BR( e01 ! Ge) is not possible even if the bino and(or) wino components are close to 1, since the Z-mode is always present. However, the h-associated decay channel can be easily suppressed with a relatively larger . Motivated by this behaviour of the BRs, we choose to work with a signal consisting of at least one photon for our collider analysis. In the ZGe decay mode has a substantial BR ( our case, the e10 being dominantly bino-like, it decays mostly into a 25%). The higgsino admixture in e10 being and a Ge. However, small, the hGe decay mode is not considered in this work. However it is worth noting that this particular channel can be the dominant mode for a higgsino-dominated NLSP and could also be an interesting mode of study, which we leave for future work. 3 Benchmark points For our analysis we choose a few benchmark points that would represent the salient features of a compressed sparticle spectrum with varying compression strengths while also categorically de ning a few points that are more in line with current SUSY searches with Ge LSP by the CMS and ATLAS collaborations at the LHC. We insure that our benchmark choices are consistent with all existing experimental constraints. We consider both compressed and uncompressed spectra, with bino-like as the LSP and warm dark matter candidate. For one of the benchmarks, we also show e01 as the NLSP and a keV gravitino { 8 { Compressed spectra Uncompressed spectra Parameters M1 M2 M3 At tan MA mg e mqL mqR e e met1 met2 m m eb1 eb2 m`eL m`eR mi represents the mass of the heaviest coloured sparticle (g=qek; (k = 1,2)) and me01 , the mass of e me01 where the e ect of an eV mass gravitino LSP. The nal benchmarks used in this study are shown in table 1. The mass spectrum and decays of the sparticles are computed using SPheno-v3.3.6 [63{ 65]. We restrict the light CP-even Higgs mass to be in the range 122-128 GeV, i.e, within 3- range of the measured Higgs mass [1{4] and including theoretical uncertainty of 4 GeV. Note that when the mass spectrum is compressed, all squark=gluino (which are nearly degenerate in mass) production channels contribute signi cantly to the signal. For all the benchmark points, the squarks and gluino decay directly or via cascades to the binolike e10 NLSP. The e10 then dominantly decays to a photon and gravitino and, to a lesser { 9 { with jets and E=T which de nes our signal. To evade constraints from photon(s) searches at the LHC for simpli ed models [41{48], we require the sparticles in a compressed spectrum such as ours, to be much heavier than the existing experimental limits. We have checked this for our spectra represented by the benchmark points, with the NLSP mass lying in the range 2:4 2:6 TeV with varied masses and hierarchy of the coloured sparticles with respect to the NLSP. Amongst them, C6 is the utmost compressed spectra, with a mass gap, Mi 6 GeV between the coloured sparticles and the NLSP of mass 2462 GeV, followed by C2, C5 where the mass gap is in the range of 40-50 GeV and the NLSP masses are 2428 and 2526 GeV respectively. We have also considered benchmarks C1, C3 and C4 such that the mass gap between the coloured sparticles and NLSP are slightly higher and lie in the range of 100-200 GeV. We also choose various possible mass hierarchical arrangements of the squarks and gluino to accommodate di erent cascades contributing to the signal. For example, C1 and C3 have di erent squark-gluino mass hierarchical stuctures in the strong sector. This leads to di erent jet distributions in the two cases. C2 and C5, on the other hand, are similar in the arrangement of the sparticles, however placed within 50 GeV from the NLSP, which represents a much more compressed scenario. Finally we consider two uncompressed spectra U1, U2 with NLSP mass 700 GeV and 1200 GeV and gluinos with mass 1.4 TeV and 1 TeV above the NLSP respectively. Since the photons arise from the NLSP decays, a heavier NLSP gives rise to a harder photon, having better chances of passing the analysis cuts. Thus the di erence in the signal cross-sections di er on account of the di erence in hardness of the photons and the resulting cut e ciencies in these two cases. Benchmark points U1, U2 are in fact replications of the simpli ed scenarios that are considered by experimental collaborations to put limits on SUSY particle masses. For both these benchmark points, we have kept the squarks very heavy ( 4 5 TeV) so that the gluino pair production is the only dominant contributing channel. However, we have only focussed on uncompressed spectra with event rates comparable to those of the compressed spectra. Since the large mass gap between the gluino and NLSP allow for multiple hard jets to be produced as opposed to the compressed case, we further exploit this feature to di erentiate compressed from uncompressed scenarios with comparable event rates during signal analysis. 4 Collider analysis We look for multi-jet signals associated with very hard photon(s) and missing transverse energy (E=T ) in the context of SUSY with gravitino as the LSP. For such GMSB kind of models with a keV gravitino, a very clear signature arises from the decay of the NLSP neutralino into a photon and a gravitino. If the NLSP-LSP mass di erence is large enough, two hard photons would appear in the nal state at the end of a SUSY cascade. The lightest neutralino, if bino-like, decays dominantly into a photon and gravitino ( 75%) while a small fraction decays into Z boson and gravitino ( 25%). For cases with e10 having a signi cant higgsino component, we get comparable branching fractions for its decay into Z boson or a Higgs boson, besides photons, along with Ge. For simplicity, we have considered a bino-like e01 as the NLSP. Note that the signal strength consisting of very hard photons in the nal state can be a ected by the composition of the NLSP as we have discussed before. The e01 decay into a Z Ge however still remains relevant for the bino-like e10 and as a result, gives rise to a monophoton signal at the LHC along with the diphoton channel, associated with large missing transverse energy. The existing LHC constraints in such scenarios have easy to detect and also highly e ective to suppress the SM background events. already pushed the e01-qe-ge mass bounds above 1.5 TeV which automatically result in a large e01 - Ge mass gap. This gives rise to very high pT photons in the nal states, which are very In this work, we consider six benchmark points for compressed spectra (C1 - C6) (m 01 0 such that the entire coloured sector (apart from et2 and eb2) lie within 200 GeV of the e1 2.4 - 2.6 TeV). We then estimate signal rates of nal state events with at least one or more hard photons arising from all possible squark-gluino pair production modes. We also study a couple of uncompressed spectra (U1,U2) such that both the compressed and uncompressed spectra produce similar event rates for our signal. In these spectra, the NLSP mass is around 700 and 1200 GeV respectively and the gluino is the lightest coloured sparticle having a large ( 1-1.4 TeV) mass gap with the NLSP. The squarks are chosen to be heavier (4-5 TeV) and are essentially decoupled from rest of the spectrum. The large mass gap between the NLSP and the coloured sector ensures multiple hard jets from their decay cascades besides the hard photons. Thus with di erent mass gaps and squark-gluino hierarchy among the compressed and uncompressed spectra, the jet pro les are expected to be signi cantly di erent for the benchmark points. Following the existing ATLAS analysis [48], which provides the most stringent constraint on the SUSY spectrum with a light gravitino LSP, we determine the signal event rates for our choice of benchmark points. Since we have also chosen compressed and uncompressed spectra such that the nal state event rates are equal or comparable after analysis, it is a priori di cult to determine which scenario such a signal re ects. Keeping this in mind, we propose a set of kinematic variables, besides the usual kinematic ones like E=T and MEff , which highlight the distinctive features of compression in a SUSY spectra over an uncompressed one with Ge as the LSP, although both have comparable signal rates. 4.1 Simulation set up and analysis cles at p s = 13 TeV LHC. Parton level events are generated using Madgraph5 (v2.2.3) [66, We consider the pair production and associated production processes of all coloured sparti67] for the following processes with upto two extra partons at the matrix element level: p p ! qe qe; qege; qeqe; qe qe ; qe ge; ge ge We reject any intermediate resonances at the matrix element level, which may arise in the decay cascades of the sparticles from two or more di erent processes, to avoid double counting of Feynman diagrams to the processes. The parton level events are then showered using Pythia (v6) [68]. To correctly model the hard ISR jets and reduce double counting of HJEP09(217)6 jets coming from the showers as well as the matrix element partons, MLM matching [69, 70] of the shower jets and the matrix element jets have been performed using the shower-kT algorithm with pT ordered showers by choosing a matching scale (QCUT) 120 GeV [71]. The default dynamic factorisation and renormalization scales [72] have been used in Madgraph whereas the PDF chosen is CTEQ6L [73]. After the showering, hadronisation and fragmentation e ects performed by Pythia, subsequent detector simulation of the hadron level events are carried out by the fast simulator Delphes-v3.3.3 [74{76]. The jets are reconstructed using Fastjet [77] with a minimum pT of 20 GeV in a cone of R = 0:4 using the anti -kt algorithm [78]. The charged leptons (e; ) are reconstructed in a cone of R = 0:2 with the maximum amount of energy deposit allowed in the cone limited to 10% of the pT of the lepton. Photons are reconstructed in a cone of R = 0:4, with the maximum energy deposit in the cone as per ATLAS selection criteria [48]. For background estimation, we focus on the most dominant SM backgrounds for photon(s) + jets + E=T signal at 13 TeV LHC, such as: + 4 jets, + 3 jets, W + 3 jets, Z + 3 jets and tt + jets. The sort of extremely hard pT photons that we expect in our signal events, are unlikely to be present in SM processes in abundance and the hard photons will arise mostly from the tails of the pT distributions. Hence in order to obtain a statistically exhaustive event sample, we choose a hard pT > 200 GeV cut as a preselection for the parton level events for the leading photon while generating the background events. For MLM matching of the jets, the matching scale was chosen in the range 30-50 GeV as applicable for electroweak SM processes. Some other SM processes, such as QCD, tt+jets, W +jets, Z+jets, in spite of having no direct sources of hard photons, may also contribute to the background owing to their large production cross-sections coupled with mistagging of jets or leptons leading to fake photons. However, the cumulative e ect of hard pT as well as E=T and MEff requirement renders these contributions negligible. Primary event selection criteria. We identify the charged leptons (e; ), photons and jets as per the following selection criteria (A0) for signal and background events alike: Leptons (` = e; ) are selected with p`T > 25 GeV, j ej < 2:37 and j j < 2:70 and excluding the transitional pseudorapidity window 1:37 < j `j < 1:52 between the ECAL barrel and end cap of the calorimeter. Photons are identi ed with pT > 75 GeV and j j < 2:47 excluding 1:37 < j j < 1:52. Reconstructed jets have pjT > 30 GeV and lie within j j j < 2:5. All reconstructed jets have a large azimuthal separation with E~= T , given by (j~et; E~= T ) > 0:4 to reduce fake contributions to missing transverse energy arising from hadronic energy mismeasurements. The jets are separated from other jets by Rjj > 0:4 and from the reconstructed photons by R j > 0:4. Benchmark Points With these choices of nal state selection criteria we now proceed to select the events for our analysis. Signal region: 1 + > 2 jets + E=T . We look into nal states with at least 1 photon, multiple jets and large E=T . Amongst the existing analyses for the same nal state carried by the experimental collaborations, the ATLAS analysis imposes a more stringent constraint on the new physics parameter space and hence we have implemented the same set of cuts as enlisted below for our analysis: A1: the nal state events comprise of at least one photon and the leading photon ( 1) must have pT1 > 400 GeV. A2: there should be no charged leptons in the nal state (N`=0) but at least 2 hard jets (Nj > 2). (j; E=~T ) > 0:4. A3: the leading and sub-leading jets must be well separated from E=~T , such that A4: the leading photon must also be well separated from E=~T with ( 1; E=~T ) > 0:4. A5: as the light gravitinos would carry away a large missing transverse momenta, we demand that E=T > 400 GeV. A6: we further demand e ective mass, MEff > 2000 GeV, with MEff = HT + GT + E=T , where HT = i pT (ji) is the scalar sum of pT of all jets and GT = j pT ( j ) is the scalar sum of pT of all photons in the event. In table 2 we have summarised the e ect of the cuts A0-A6 for our signal on the respective benchmark points. All the production cross-sections in the table is scaled using NLO+NLL K-factors obtained from NLL Fast [79{83]. As evident from table 2, cut e ciencies vary depending on the compression in the spectra. For example, the jet requirement a ects the signal cross-section of C6 the most, { 13 { Luminosity L (in fb 1) for C1 C25 C3 C4 C5 C6 U1 U2 the 13 TeV run of the LHC corresponding to the benchmark points. since it is the most compressed spectra among all. Naturally, one would expect jet multiplicity to be smaller in this case compared to the others. As a result, the requirement Nj > 2 reduces the corresponding signal cross-section by a signi cant amount, whereas, for the uncompressed spectra, U1 and U2, this cut has no bearing. The hard photon(s) in the signal events and the presence of direct source of E=T ensure that the E=T and MEff cuts are easily satis ed by the selected events. For the corresponding background events, we use the observed number of background events at ATLAS, which is 1, for the same nal state studied at an integrated luminosity of 13.3 fb 1 at 13 TeV [48]. The statistical signal signi cance is computed using r h S = 2 (s + b) ln 1 + s b s i where s and b represent the remaining number of signal and background events after implementing all the cuts. In table 3, we have shown the required integrated luminosity to obtain a 3 and 5 statistical signi cance for our signal corresponding to all the benchmark points. The required luminosity for 3 and 5 statistical signi cance varies depending on the relative compression and heaviness of the spectra. As evident, C2 has the best discovery prospects and is likely to be probed very soon. C6 on the other hand, despite of having a similar squark-gluon spectra and a very similar production cross-section to that of C2, requires a much larger luminosity ( 112 fb 1) to be probed. This is because the high amount of compression in the spectra reduces the cut e ciency signi cantly due to the jet multiplicity requirement. The required integrated luminosity for C1 and C5 is very similar although C5 has a relatively lighter coloured sector and thus a larger production cross-section compared to C1, as can be seen from table 2. However, the photon and jet selection criteria reduces the C5 cross-section making it comparable to that of C1. The situation is di erent for U1 which despite of having the lightest gluino, requires the largest 5On the face of it, this benchmark may be ruled out by the current searches at LHC. However, this is to be taken with some caution, since the search criteria suggested by us are slightly di erent from the ones used in the current experimental searches. HJEP09(217)6 luminosity ( 326 fb 1) among all the benchmark points in order to be probed. The reason is two-fold. Firstly, the production cross-section in this case (and also for U2) is comprised with a much smaller luminosity ( of just the gluino-pair since the squarks are far too heavy to contribute. Secondly, the e01 being and hence the photon selection criteria further reduces the signal cross-section. A similar 700 GeV, the photons arising from e10 decay are relatively on the softer side squark-gluon spectra in presence of a heavier e10 (U2) therefore is likely to be probed 139 fb 1) than U1. Thus it is evident from table 2 and 3, that given the present experimental constraints, a compressed spectra, unless it is too highly compressed such that the cut e ciency is reduced signi cantly, can improve the squark-gluino mass limits by a signi cant amount. For example, C2 can be probed with slightly little more luminosity than 13.3 fb 1 but with a coloured spectra that lies in the vicinity of 2.5 TeV. This clearly suggests that a compressed spectra becomes much more quickly disfavoured over an uncompressed spectra with a gravitino LSP contrary to the case where a compressed SUSY spectrum appears as a saviour of low mass SUSY with a neutralino LSP. This is because of the hard photons that themselves act as a clear criterion to distinguish the signal over the SM background. 4.2 Distinction of compressed and uncompressed spectra Given the inclusive hard photon + E=T signals, supposedly due to a light gravitino, can one ascertain whether the MSSM part of the spectrum is compressed or uncompressed? With this question in view, it is worthwhile to compare signals of both types with various degree of compression in presence of a light ( keV) gravitino as the LSP. We show that the kind of compressed spectra we have used enhances the existing exclusion limit on the coloured sparticles. We consider di erent squark-gluino mass hierarchy represented by our choice of some sample benchmark points presented in table 1. The Ge being almost massless in comparison to the e01 in consideration, the photons generated from the e01 decay into Ge are always expected to be very hard for both the compressed and uncompressed scenarios. This feature can be used to enhance the signi cance of the signal irrespective of the associated jets in the event. We provide a framework where one can use the properties of these jets in a novel way to distinguish between the two di erent scenarios in consideration even if they produce a similar event rate at the LHC. For illustration, let us consider the benchmark points, C5, C4 and U2 all of which result in nearly identical event rates for our signal and thus it is di cult to identify whether it is a signature of a compressed or an uncompressed spectra. It would be nice to have some kinematic variables which could be used to distinguish among the di erent kind of spectra. Subsequently, we have proposed few such variables which show distinctive features in their distributions depending on the relative hardness and multiplicity of the nal state photon(s) and jets. An uncompressed spectrum, such as U2 is characterized by a large mass gap between the strong sector sparticles and the NLSP ( e01). This ensures a large number of high pT jets from the cascades as compared to C5 and C4. The di erence in jet multiplicity in the two cases is clearly visible in gure 4 where we have presented both the jet and photon multiplicity distributions for some sample compressed and uncompressed spectra. HJEP09(217)6 C5 and U2 representing moderately compressed, highly compressed and uncompressed scenarios respectively. Figure (a) has been prepared after implementing the selection cuts A0+A1 and gure (b) after A0. The hard photons in the event are originated from the e10 decay and since for all our benchmark points the e10 is su ciently heavy, the photon multiplicity peaks at a similar region for both the compressed and uncompressed spectra. However, the jets in the case 0 of U2 are generated from the three body decay of the gluino into a pair of quarks and e1 . As evident from gure 1, for the choices of the sparticle masses of U2, the other decay mode is highly suppressed. Hence one would naturally expect to obtain a large number of jets in the nal state as shown in gure 4. C5 having a high degree of compression ( Mi = 48 GeV) in the parameter space results in least number of jets in the nal state. C4, on the other hand, has a more relaxed compression ( Mi = 198 GeV) that gives rise to slightly harder cascade jets passing through the jet selection criteria resulting in a harder distribution than C5. The relative di erence in the compression factor ( Mi) among the three benchmark points are also visible in the jet pT distributions shown in gure 5. As expected, the leading ( gure 5(a)) and subleading ( gure 5(b)) jet pT distributions predominantly show a harder peak for U2 as compared to C4, C5. However, hard jets may also arise from the e01 decaying to a Z boson and gravitino (BR two jets. The Z boson is expected to be highly boosted and thus one can easily obtain additional hard jets from its decay. These jets populate a small fraction of the total number of events and thus for a compressed spectra one of these jets can turn out to be the hardest jet in the event. This feature can be observed by the subdominant peak at 1000 GeV for 25%) as the Z decays dominantly into the leading jet pT distribution in gure 5. Figure 5(c) and (d) show the leading and subleading photon pT distributions respectively for C4, C5 and U2. The e01 mass in C4, C5 being from their decay are much harder than the leading jets in the spectra as opposed to the uncompressed spectra (U2) and hence, the peak in the photon pT distribution is signif 2.5 TeV, the photons produced { 16 { points representing various compressed (C4), more compressed (C5) and uncompressed (U2) spectra after implementing the selection and analysis cuts A0{A6. icantly shifted to lower values. Thus while the total hadronic energy, HT ( gure 6(a)) peaks at a higher value for the uncompressed case owing to a large number of hard jets, GT ( gure 6(b)) which is the scalar sum of all photon pT , peaks at a lower value for the uncompressed case than the compressed cases. Among other kinematic variables, one can also look into the E=T and MEff distributions to distinguish the compressed and uncompressed scenarios as shown in gure 6(c) and (d) respectively. Since the photons are almost always harder for the compressed spectra compared to the uncompressed cases, we have observed that the E=T , required to balance the total visible transverse energy, is much harder for the former. E ective mass, MEff de ned as the sum of HT , GT and E=T , also shows some small di erence in the peak value for both cases. In U2, GT and E=T are softer than that for C4, C5 but HT is much harder resulting in the MEff peaking at similar values for the both cases. However, since the photons are considerably harder than the jets in all cases, the e ect being more pronounced for the compressed over the uncompressed case, the MEff distribution falls faster for U2 than C4 and C5 as can be seen from gure 6(b) and 6(d) respectively. GT , missing transverse energy E=T and E ective Mass MEff , for benchmark points representing various compressed (C4), more compressed (C5) and uncompressed (U2) spectra after implementing the selection and analysis cuts A0{A6. Taking cue from the kinematic distributions in gure 5 and gure 6, we now proceed to formulate two observables r1 = pT (j1) pT ( 1) and r2 = pT (j2) pT ( 1) which capture the essence of the jet and photon transverse momenta behaviour in a way as to distinctly distinguish between the compressed and uncompressed scenarios. As seen in gure 7, for the compressed case, r1 ( gure 7(a)) peaks at rather small values ( 0:1 ) than the uncompressed case ( 1:0) since the leading jet pT is almost always softer than the leading photon for compressed spectra whereas for the uncompressed case there are hard jets with pT values comparable to the leading photon pT . However for the compressed spectra, the collimated hard jet from the highly boosted Z boson produced in the decay of the e10, lead to a subdominant peak at constructed with the sub-leading jet and leading photon pT , peaks at lower values ( 0:1) for C4 and C5 since the sub-leading jet, coming from the cascades or ISR in the 0:7 in r1. The observable r2 ( gure 7(b)) compressed case is expected to be much softer than the photon. For U2, r2 peaks at 0:5 since the sub-leading jet also coming from the cascade is softer than the hardest photon. Thus we nd that the above ratios seem to enhance the two major distinctive features between a compressed and an uncompressed scenario, namely the high/low pT for the photon/jet for the compressed as compared to the low/high pT of the photon/jet for the uncompressed case. We further note that the jet multiplicity is another variable which shows a di erence in the distributions for compressed spectra C4 and C5 when compared to that of the uncompressed spectra U2 ( gure 4(a)). Although the choice of our signal region involves HJEP09(217)6 Nj > 2, the compressed spectra, C4 and C5, still retain a su cient fraction of events with higher number of jets. In contrast, the uncompressed spectra U2 has larger number of hard jets for all events, and thereby remains mostly una ected by this selection criterion. We therefore de ne a modi ed ratio (scaled by the jet multiplicities) as r10 = Nj r1 and r20 = Nj r2: Notably the new variables r10 and r20 are able to signi cantly enhance the di erences between a compressed and uncompressed spectra. Since the scale factor, Nj , is always greater for the uncompressed spectra U2 than for the compressed spectra C4 and C5, we nd the peak values of r10 ( 4.0) and r20 ( 2:5) of the uncompressed spectra are shifted further away from that of compressed ones (r10 0.2-0.5 and r20 0.1-0.3). Quite importantly the visible overlap seen in r1 for the sub-dominant peak is now completely disentangled in the new variable r10 as seen in gure 7(c). This is signi cant in the sense that when the event samples would retain a much harder criterion for the leading jet then the events for U2, C4 and C5 would all feature the overlap observed for the sub-dominant peak while the di erence for low r1 might be washed away for this particular choice of event selection. Besides enhancing the di erences between the compressed and uncompressed spectra, the di erential distributions in ri and ri0 can also be used to highlight the di erences amongst the di erent compressed spectra themselves, depending on the level of compression in mass. For example, C4, has a larger mass separation Mi than C5, and shows a peak in the jet multiplicity at Nj = 3 while for C5, the peak value of the di erential cross section is at Nj = 2. Thus a larger fraction of events survive after analysis for C4 than C5. Again, since C5 is relatively more compressed than C4, the jets from C4 are considerably harder than the latter. However the NLSP mass for C4 is larger than C5, since to probe lower values of compression, we require a heavier NLSP to meet current LHC bounds. This results in the photons being harder for C4 than for C5. The combined e ect of the two seem to be more prominent for both r1 and r10, where the leading jet is either the ISR jet or cascade jet in case of C4. For r2 this e ect seems neutralised, owing to the sub-leading jets for both cases, being much softer than the leading photon pT . However the scale factor Nj shifts the peak value of r20, thus e ciently distinguishing amongst the two compressed spectra of varying degree of compression. compressed and uncompressed scenarios for some of the benchmark points representing various compressed (C4), more compressed (C5) and uncompressed (U2) spectra after implementing the selection and analysis cuts A0{A6. 4.3 eV gravitino As pointed out earlier that the kinematic characteristics of events when the NLSP decays into a gravitino are independent of whether the Ge is in the keV or eV range. Therefore, for an NLSP decaying into a Ge and a SM particle, the Ge is practically massless. However, as discussed in section 2.1, a lighter gravitino has a stronger coupling strength to the sparticles. Thus the decay of the sparticles into a SM particle and gravitino dominates over its decay to the NLSP. For a gravitino of mass 1 eV, we nd that the gluino/squark almost always directly decays to the gravitino rather than to the NLSP. The branching fractions also depend on the mass gap between the coloured sparticles and the NLSP. These features are highlighted in gures 1 and 2 where both compressed and uncompressed mass gaps are shown. Therefore, an eV Ge does a ect the overall event rates of the signal in the photon channel when compared to the keV Ge case. An immediate consequence which has gone unnoticed for such light eV Ge case would be a new competing signal which can become C1 cross-section (in fb) Cross-section (in fb) after cuts: A0+A1 more relevant than the more popular photonic channel. This can be easily understood by taking a look at the resulting BR(ge ! gGe) for some of our benchmark points in presence of an eV gravitino. As indicated by gure 1, this branching ratio is supposed to go up if the spectrum is more compressed. For the same benchmark points as in table 1, now in the presence of an eV Ge, we have observed that BR(ge ! gGe) (Asmageceo01n=seq1u4e0n3cGe,eCV)1, wUi2th( anmegeVe01g=rav9i1t1inGo,e Vis)uannldikeCly1 t(o ymiegelde01a=go7o8dGeevVe)ntrersapteecitnivethlye. 13%; 41% and 99% for U1 photonic channel since the gluino avoids decaying into the NLSP altogether. However, a small fraction of the squarks may still decay into the NLSP, 4% and 24% precisely for left and right squarks respectively. Hence, one would still expect a photon signal for such a scenario, but a much weaker one as presented in table 4. As expected, the photon signal weakens considerably when compared to one with a keV gravitino and requires an integrated luminosity 1000 fb 1 for observation at the LHC. However, much stronger signal would be obtained in the \n-jet+E=T " (n 2) channel as the nal state would have at least two very hard (pT 's exceeding more than a TeV) jets and an equally hard E=T signal for the eV-gravitino case. The conventional multi-jet search [31] rely upon the usual E=T , MEff , pHT E=T and to reduce the SM backgrounds. We have checked that with these cuts, a 3 signi cance can be achieved for C1 in the \n-jet+E=T " (n 2) nal state at an integrated luminosity of 1000 fb 1. However, in the presence of an eV gravitino, one can demand harder pT requirements of the jets and harder E=T , MEff along with the other conventional cuts to increase signal signi cance further. We have checked that one can easily bring down the required luminosity to 728 fb 1 for a 3 signi cance, which is a big improvement over the results obtained for the photon-associated nal state. Thus the multi-jet channel is the more favorable one in order to explore an eV gravitino in presence of a TeV compressed colour sector. However, as mentioned earlier, such a light gravitino may not be a viable dark matter candidate and would necessarily require the presence of other candidates to (j; E=~T ) cuts and in some cases, razor variables [32] satisfy the constraints. 5 Summary and conclusion In this work, we have explored the compressed SUSY scenario in the presence of a light gravitino LSP within the framework of phenomenological MSSM. The question asked is: since the light gravitino produced in the (neutralino) NLSP decays generates as much E=T for compressed spectra as for uncompressed ones, are the former discernible? HJEP09(217)6 The existing collider studies for such scenarios mostly account for the uncompressed parameter regions, and in some cases the NNLSP-NLSP compressed regions. However, compression in the entire coloured sector of the sparticle spectrum can result in signi cantly di erent exclusion limits on the masses of squark, gluino and the lightest neutralino. The presence of a light gravitino in the spectrum a ects the branching ratios of the coloured 0 sparticles into e1 . We have studied the interplay of these relevant branching ratios for e1 varying Ge mass and di erent amount of compression in the rest of the sparticle spectrum for a bino-like 0. Dictated by the DM constraints, we have mostly concentrated on the keV Ge scenario and have performed a detailed collider simulation and cut-based analysis for photon + > 2 jets + E=T nal states arising from the squark-gluino pair production channels 1 in the context of the LHC. In our case, the squarks and the gluinos dominantly decay into the e01 which further decay into a Ge along with a nal state. Hard pT photon requirement can be used along with other kinematic cuts to suppress the SM background very e ectively. We have followed the existing ATLAS analysis for the same nal state with the help of some benchmark points. We have shown that with the existing experimental data, the exclusion limits on the coloured sparticle masses can increase by 500 GeV for a highly compressed sparticle spectra. It is understood that similar signal event rates can be obtained from both uncompressed and compressed spectra depending on the choices of masses of squark, gluino and the lightest neutralino. However, the di erence in the compression will be re ected in the kinematic distributions of the nal state jets and photons. We have exploited this fact to construct some variables which can be used to good e ect to di erentiate between the two scenarios. We have also studied the collider prospects of SUSY spectra in the presence of sub-keV gravitinos. It turns out that in such cases, the Ge-associated decay modes of the heavy ( 2.5 TeV) coloured sparticles start to become relevant in the presence of high compression between the NNLSP and NLSP. Then the most suitable nal state to look for such spectra would be multi-jets + E=T . However, the existing DM constraints strongly disfavour presence of or a Z resulting in the above mentioned such light gravitino in the spectrum. Acknowledgments The work of JD, SM, BM and SKR is partially supported by funding available from the Department of Atomic Energy, Government of India, for the Regional Centre for Acceleratorbased Particle Physics (RECAPP), Harish-Chandra Research Institute, HBNI. PK thanks RECAPP for the hospitality during this work. Computational work for this work was carried out at the cluster computing facility in the Harish-Chandra Research Institute Open Access. 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Juhi Dutta, Partha Konar, Subhadeep Mondal, Biswarup Mukhopadhyaya, Santosh Kumar Rai. Search for a compressed supersymmetric spectrum with a light gravitino, Journal of High Energy Physics, 2017, 26, DOI: 10.1007/JHEP09(2017)026