Closing in on compressed gluino-neutralino spectra at the LHC

A huge swath of parameter space in the context of the Minimal Supersymmetric Standard Model (MSSM) has been ruled at after run I of the LHC. Various exclusion contours in the $m_{\tilde{g}}-\m_{\tilde{\chi}_{1}^{0}}$ plane were derived by the experimental collaborations, all based on three-body gluino decay topologies. These limits are however extremely model dependent and do not always reflect the level of exclusion. If the gluino-neutralino spectrum is compressed, then the current mass limits can be drastically reduced. In such situations, the radiative decay of the gluino $\gino \ra g \neut{1}$ can be dominant and used as a sensitive probe of small mass splittings. We examine the sensitivity of constraints of some Run I experimental searches on this decay after recasting them within the \texttt{MadAnalysis5} framework. The recasted searches are now part of the \texttt{MadAnalysis5} Public Analysis Database. We also design a dedicated search strategy and investigate its prospects to uncover this decay mode of the gluino at run II of the LHC. We emphasize that a multijet search strategy may be more sensitive than a monojet one, even in the case of very small mass differences.

1 Introduction and motivation parity conserving scenarios, if the lightest SUSY particle (LSP) is massive and degenerate with the squarks and/or gluinos, the so-called "compressed" SUSY scenarios, these limits can be seriously weakened [14][15][16][17][18][19][20]. As far as the official experimental analyses are concerned, published gluinos mass limits in the SMS approach were obtained mainly from its three-body decaysg → qqχ 0 1 , where the final states quark can be of any flavour [6,[21][22][23][24][25] org → qq ′χ± 1 [6,21]. Provided the gluinoneutralino spectrum is compressed, the limits derived from three-body decays involving heavy-flavours do not apply and only the ones with light-flavours in the final states can give a handle on this situation. However, as limits on the first and second generation of squarks are quite strong, theg → qqχ 0 1 modes with light quarks may be heavily suppressed. Furthermore, as already stressed, a large part of the parameter space feature a compressed spectra to evade the stringent bounds from the LHC, and few SMS interpretations fully encompass this situation for the gluino. In compressed scenarios, initial state radiation (ISR) in the form of jets which recoil against the missing momentum of the LSP may be used to discover or place bounds on the model. This method has been used to set mass limits on squarks and gluinos [6,[14][15][16][17][18][19][20][26][27][28][29][30] and third generation squarks [14,29,[31][32][33][34][35].
In the case where the three body decays are kinematically forbidden or suppressed, there exists another decay pattern available for the gluinos to decay into, which has received very little attention so far, but could fill the small mass difference gap: that of the two-body radiative decayg → gχ 0 i . In a CMSSM-inspired scenario, since the mass difference ∆M = mg − mχ0 1 is fixed from conditions imposed at the GUT scale, when mg increases, so does ∆M. In turn, the decay width of the gluino will be dominated by the three-body decays. Unlike GUT constrained SUSYscenarios, general explorations of the MSSM may exhibit significant portions of parameter space where the radiative decayg → gχ 0 1 can be competitive with three-body decays [36][37][38][39][40][41][42][43][44][45]. Within these specific regions, significant branching fractions of the gluino radiative decay are characterised by a spectrum with heavy squarks. Thus, the direct two-body decaysg →qq are forbidden andg → qqχ 0 i are suppressed by the heavy scalar quark mass, leaving the loop-induced decay as the only available mode to decay into. Therefore, for compressed gluino-neutralino scenarios, the gluino loop decay can be used as a sensitive probe and improve the current limits. A spectrum with decoupled scalars and lighter gauginos and higgsinos is not unexpected in SUSY models like (mini) Split-SUSY/PeV scale SUSY [46][47][48][49][50][51][52], Spread SUSY scenarios [53] or pure gravity mediation [52,[54][55][56]. Moreover, a Higgs mass around 125 GeV implies a non-negligible branching fraction of the gluino loop decay when tan β ≃ O(1) [43]. It is worth mentioning that if the scalar superpartners are heavy enough, then the gluino lifetime τg can be sufficiently large to lead to displaced vertices or even hadronise into Rhadrons [49,50,57,58]. Nevertheless, ifm O(10 4 ) TeV, τg is too small such that the gluino decays promptly in the detector [43]. To obtain a compressed gluino-neutralino spectrum, given a SUSY-breaking scheme, one needs non-universalities in the gaugino sector at the GUT scale to obtain a small ∆M. In the context of non-universal supergravity (NUSUGRA) models, the gluino can be in a significant part of the parameter space the next-to-lightest SUSY particle (GNLSP) and the neutralino the LSP [59][60][61][62][63][64][65][66]. A non-exhaustive list of other SUSY models accommodating the GNLSP scenario include left-right symmetric model with gravity mediated SUSY breaking [67][68][69][70], pure gravity mediation/mini-split SUSY [52,56] and general gauge mediation [71]. Besides being a discovery mode for the gluino, its loop-decay has some other merits from the phenomenological perspective. Indeed, since squarks contribute to the radiative decay through loop diagrams, the two-body decaysg → gχ 0 i carry important information about the scalar mass scalem [43], which would be otherwise inaccessible in scenarios with decoupled scalars. Moreover, in GNLSP models, the LSP can account for the relic density of dark matter through its coannihilation with the gluino. The efficiency of such processes crucially depends on the gluino-LSP mass difference ∆M. Thus, measuring or constraining this splitting, only accessible at collider experiments, is essential to estimate the phenomenological viability of these models. We should also note in passing, that in models with spontaneously broken global supersymmetry the radiative decayg → g G, where G is the gravitino, is also possible. It can be dominant when the original scale of supersymmetry breaking √ F is of the same order of the squark mass scale m [42,48,[72][73][74][75][76][77][78][79], whatever the mg − m G mass difference. Depending on the value of F the gluino can decay promptly, in flight inside the detector, or be long-lived. For very long-lived gluinos, ATLAS and CMS have excluded charged R-hadrons with a mass less than 1.3 TeV [80,81], if they escape the detector, or less than 850 GeV [57] if stopped in the detector. If metastable, the gluino is excluded up to mg = 850 GeV for decays to qqχ 0 1 /gχ 0 1 , for a lifetime of 1 ns and mχ0 1 = 100 GeV [82]. A work probing scenarios where the LSP and the gluino are almost degenerate was recently performed in [29]. However, the limits derived there solely considered the three-body decays of the gluino into light-flavour quarksg → qqχ 0 1 , but with light sbottoms and light stops in the spectrum. As we will review in the forthcoming sections, the radiative decayg → gχ 0 1 is favoured when light stops are present and should dominate instead. Therefore, investigating rather the gluino loop-induced decay seems better motivated from a phenomenological point of view when all scalars are heavy and ∆M small. The ATLAS collaboration has also recently provided, using only a hadronic search that we reimplemented for this work, some results on the radiative gluino decay in [6]. Yet, results have only been presented for a fixed gluino mass mg or fixed LSP mass mχ0 1 , but not in the full mg − mχ0 1 plane. In this work, we aim at quantifying to which extent the radiative gluino decay can constrain, using Run I monojet and multijets analyses, the region where the mass splitting ∆M = mg − mχ0 1 is small, assuming a SMS interpretation where BR(g → gχ 0 1 ) = 100%. We argue in the next section, after investigating the parameter space where the loop decay is important, why a somewhat lighter third generation squark spectrum is desirable to enhance this decay from the phenomenological MSSM (pMSSM) point of view. We use the MadAnalysis5 [83,84] framework to derive exclusion contours in the mg − mχ0 1 plane, deduced from a Simplified Model approach, after recasting ATLAS and CMS monojet and multijets analyses. We provide in our work a full quantitative exploration of this plane and the quoted ATLAS 95% CL upper bound [6] for fixed mg and mχ0 1 rather serves to us as a cross check on our results, which give us quite confidence in our procedure with which we derived our own mass limits. These recasted analyses are now available on the MadAnalysis5 Public Analysis Database (PAD) [85]. The last section is devoted to the determination of a search strategy at 13 TeV to investigate the prospects for discovering the gluino through its radiative decay at run II of the LHC and then we conclude.

Phenomenology of the radiative gluino decay
In this section we review the gluino decays in a heavy scalar scenario. When the squarks are heavier than the gluino, the latter can undergo three body decays into a pair of quarks and a neutralino or chargino through an off-shell intermediate squark, or decay radiatively into a gluon and a neutralino,g → q +q +χ 0 whereχ 0 i (i = 1 . . . 4) andχ ± j (j = 1, 2) are neutralinos and charginos respectively. Let us first review the radiative two body decays of the gluino, which occur via quark-squark loop diagrams (Fig. 1). The neutralinoχ 0 i is an admixture of wino-( W 3 ), bino-( B) and Figure 1: Diagrams relevant for the radiative gluino decay. Since the gluino is a Majorana fermion each diagram is accompanied with a similar one but with the internal arrows reversed.
higgsino-like ( H) neutral spinors, which are respectively the superpartners of the neutral gauge eigenstates B, W 3 and of the two Higgs doublet of the MSSM H u,d , If the squarks are very heavy, from an effective Lagrangian point of view the decay width into a wino is strongly suppressed since it is induced by a dimension 7 operator [42,43], whereas for a bino or a higgsino it can be induced already by a dimension 5 chromo-magnetic interaction, where m is an effective squark mass scale. The partial widths of these two body-decays are given by [36,42,43,69], in the heavy squark limit, where α and α s are the electromagnetic and strong couplings constants respectively. We used the short-hand notations c W ≡ cos θ W , s W ≡ sin θ W , s β ≡ sin β. The angle θ W is the weak mixing angle and β is defined through the ratio tan β = v u /v d where v u,d are the vacuum expectation values of the two SU(2) L Higgs doublets H u,d of the MSSM. Both angles lie between 0 and π/2. Y q , appearing in Eq. 6, is the quarks hypercharge where the index q runs through all flavours. In Eq. 7, since the decay width is proportional to the top mass, only the stops-tops loops were kept. From Eq. 6 we can see that Γ(g → g B) scales like m −4 q whereas Γ(g → g H) benefits from a logarithmic enhancement. The origin of this logarithmic enhancement can be understood from an effective Lagrangian point of view as follows. In the effective theory where the squarks have been integrated out, this decay is induced by a top-top-gluino-higgsino operator in which the two top quarks form a loop which can emit a gluon to form the chromo-magnetic gluino-gluon-higgsino interaction of Eq.5. Such a diagram is divergent in the effective theory thereby generating a logarithmic enhancement [36,42], which is cut-off by the squark mass (the scale of the effective theory breakdown). Therefore this decay is an interesting probe of the scalar mass scale in case they are kinematically inaccessible from colliders [43]. In the very heavy squark limit the leading logarithmic corrections should be resummed to obtain reliable predictions using renormalisation-group techniques as has been done in [42]. Let us now turn on to the three body decays of the gluinog → qqχ 0 which is mediated by squark exchangeq (Fig.2), with the assumption that the squark sector respects flavour symmetries. In the massless quark limit, only the bino-like contributes and we can get añ  analytical expression of the gluino partial decay width [39,42,43,69], where f (x) = 1 − 8x − 12x 2 ln x + 8x 3 − x 4 and g(x) = 1 + 9x + 6x ln x − 9x 2 + 6x 2 ln x − x 3 . Like the two-body decay into the bino-like neutralino in Eq. (6), the three-body decay width scales as m −4 q L in the heavy squark limit. If the first two squarks generations are decoupled from the third one, which is quite easily achieved in SUSY since the large top Yukawa usually drives the running of third generation squark masses to lighter value than the two others, the quarks produced in the three body decays will be composed of tt, bb pairs. For generic quark masses the integration over the three-body phase space cannot be performed analytically and one must resort to a numerical integration. However, keeping only the quark mass dependence in the couplings and in the limits mχ0 ≪ mg and mg ≪ mq L , mq R , the decay rateg → qqχ 0 i [37] is given by The sum is over all quark species allowed by kinematics. The a, b, c coefficients are given by where u ≡ u, c, t and d ≡ d, s, b. The electric charge Q q is defined as Q q = T q L 3 + Y q /2. It is then natural to ask oneself in which cases the two-body decay can dominate over the three-body one. To investigate this we define the ratio R 2/3 as Obviously, the three-body decay is suppressed by the phase space when the mass difference between the gluino and the neutralino is too small. This is particularly true forg → ttχ 0 i when the tt threshold is closed, i.e mg − mχ0 i < 2m t . In this situation the decay rates for g → bbχ 0 i may still compete with Γ(g → gχ 0 i ). In the higgisno-like case, the bb and gχ 0 i final states are dominated by the heaviest quark: the former is proportional to m 2 b and the latter to m 4 t . In the limit where the left and right squark masses are equal for each respective flavour q, i.e mq L = mq R =m q , using Eqs. (7) and (9) and defining x t = m 2 t /m 2 t , one finds for R 2/3 [37] In the bino-like case, we would obtain a similar formula using Eqs. (6) and (9), but R 2/3 only benefits from the parametric enhancementm b /m t . Hence, there are two conditions for which the two-body decay will dominate over the three-body one: • If the tt threshold is closed one needs a somewhat hierarchy between the sbottoms and the stops, • Decouple all the squarks at very high masses, in this case R 2/3 ∝ m 2 t /m 2 g [1 + ln x t ] 2 .
However, as stressed in [42], for such very heavy squarks, the logarithmic corrections have to be resummed and in the case of all squarks masses being equal and large, the resummation tends to decrease R 2/3 compared to Eq. (13) when the common scalar mass scale m 10 6 GeV. On the other hand, in the bino-like case, R 2/3 does not benefit from such parametric enhancements. The lack of logarithmic enhancement for the two-body decay (i.e the higgsino-like neutralino is not allowed in gluino decays) implies that the three-body will generally dominate instead, if available. It is worth adding that in the pure higgsino case, it is rather another three-body decay which rival with the gluino loop decay, namelyg → tb/tbχ ± 1 . This is due to the fact that the neutral and charged higgsinos are almost degenerated in mass, and this decay will dominate only once the tb/tb threshold is crossed, i.e mg − mχ0 1 ≃ mg − mχ± 1 > m t + m b . These three-body decays do not suffer from a hierarchical third generation squark spectrum since they are mediated by stops. In the pure bino case this decay will be effective at larger ∆M since the lightest charginoχ ± 1 is much heavier than the bino-like LSP. In order to illustrate to which extent the radiative gluino decay can dominate over the other decay modes, without assuming any specific SUSY-breaking pattern, we performed a numerical scan within the pMSSM parameter space using SUSY-HIT [86]. In this numerical investigation we set all soft masses (sleptons and squarks) to 5 TeV and trilinear couplings A i to zero except for the third generation squarks for which we chose the following range: The parameters related to the gaugino and Higgs sector were set to • 400 GeV < M 1 , µ < 800 GeV The scalar mass scale chosen is sufficiently low such that we ensure that the gluino would decay in the detector. We picked up only points giving the SM-like Higgs mass in the range 122 GeV < m h < 128 GeV and the resulting gluino mass is driven around mg ≃ 810 GeV due to radiative corrections. We ensured that mg > mχ0 1 such that the lightest neutralino is always the LSP. We divided the surviving points of the scan into three different regions, depending on the nature of the lightest neutralino, whether it is mostly higgsino-like, bino-like or a mixed bino-higgsino. The higgsino-like (bino-like) neutralinos correspond to a higgsino (bino) fraction greater than 90%. The remaining points are an admixture of bino-higgsino like neutralinos which we dubbed as "mixed". We display in Fig. 3 the branching ratio of the two body decay of the gluino into a gluon plus the lightest supersymmetric particle (LSP) in terms of the mass difference ∆M = mg − mχ0 1 . Given the nature of the spectrum, only the radiative decaysg → gχ 0 i and the three-body modes into heavy quarks (g → bb/ttχ 0 i andg → tb/tbχ ± 1 ) are allowed. The colour shading correspond to the level of hierarchy between the lightest stop t 1 and lightest sbottom b 1 given by the ratio m b 1 /m t 1 . It is worth noting that in the higgsino-like case we also included the two-body decay of the gluino to the next-to-lightest neutralinog → gχ 0 2 since the mass difference between theχ 0 1 andχ 0 2 is at most ≃ 15 GeV. For such a small mass difference the next-to-lightest neutralinoχ 0 2 would decay into the LSP and soft leptons or quarks originating  Figure 3: Branching ratio ofg → gχ 0 1 in terms of ∆M = mg − mχ0 1 for a higgsino-like (top,left), bino-like (top,right) and mixed bino-higgsino (bottom) neutralino. In the higgsinolike case the branching ratio of the radiative decayg → gχ 0 2 is also included. The colour shading indicates the ratio mb 1 /mt 1 .
from the off-shell Z boson decay inχ 0 2 → Z * χ0 1 . Hence the channelg → gχ 0 2 would leave the same experimental signature of jets + MET in the detector asg → gχ 0 1 . Glancing at Fig. 3 it is clear that largest branching fractions for the radiative decay are obtained when the mass difference ∆M is small. As one could expect from the approximate formulas in Eqs. (6),(7), the branching ratio of the two body decaysg → g H 1,2 (top, left panel of Fig. 3) gives the largest branching fractions. This is due to the fact that it depends on the fourth power of the top mass, unlike the bino-like and mixed cases, see Eqs. (6), (7). In addition, the dependence on ratio m b 1 /m t 1 of the loop-induced decay is much more pronounced in the bino-like and mixed case than in the higgsino case. It is particularly true for the bino case (top, right panel) where largest branching fraction are only obtained when the hierarchy between the sbottoms and stops is significant. Moreover, the two-body decay into higgsinolike neutralinos dominate even for quite large ∆M: the radiative decay starts to fall off at ∆M ≃ 200 GeV, while for the bino-like and mixed cases they already decline at ∆M ≃ 100 GeV. The drops of the loop-induced decays can be understood from looking at Fig. 4. In this figure are displayed the branching fractions of the most important three-body decays for each nature of the LSP. The left panel features the branching ratio BR(g → bbχ 0 1 ) for bino-like or mixed neutralinos. The higgsino-like LSP case is not shown since it is negligible and buried in the two others. The right panel presents the branching fraction of the gluino decay into tb/tb final states for all three LSP natures considered. In the higgsino case (blue diamonds in the right panel of Fig. 4), a comparison with the top, left panel of Fig. 3 makes it clear that as soon as the decay into tb/tb is kinematically allowed, the branching fraction BR(g → gχ 0 1,2 ) decreases fast (for ∆M 200 GeV) and the three-body modeg → tb/tbχ ± 1 starts to take over. However, thanks to the logarithmic enhancement, the loop-decay of the gluino to neutral higgsinos still persists at large ∆M and is of order 10 − 20%. The rationale , where red squares correspond to the case where the LSP is bino-like and green stars when it is a mixed bino-higgsino. The pure higgsino case is not shown as it is negligible. The right panel displays theg → tb/tbχ ± 1 for eachχ 0 1 composition, blue diamonds points corresponds to situations where the LSP is higgsino-like, orange points and when it is mixed magenta squares.
for this decay mode to take over in the higgsino case is that, as soon as the threshold is open, it does not suffer from large suppression factors. Indeed, this decay is also mediated by stop exchange, as the loop decay is, and not suppressed by small quark masses. In the pure bino case, BR(g → tb/tbχ ± 1 ) is suppressed until larger ∆M. This is due to the parameter range we chose for the scan. Indeed, for this decay mode to be open one needs a significant mass splitting between the gluino and the lightest chargino, typically mg − mχ± 1 m t + m b . In our scan mχ± 1 is driven by the value of the parameter µ, which must still be quite large to keep the LSP bino-like. Therefore one needs to reach a significantly larger mass splitting ∆M to fulfil these requirements, compared to the pure higgsino case where mχ0 1 ≃ mχ± 1 ≃ µ. Instead, the three-body decay modeg → bbχ 0 1 quickly dominates overg → gχ 0 1 , already from ∆M ≃ 100 GeV. This occurs even when the ratio mb 1 /mt 1 is large. Again, the underlying argument is that the gluino loop decay to a bino-like neutralino does not profit from any enhancement, apart from phase space considerations. For a mixed neutralino, when ∆M increases, the suppression of the radiative decay is counter-balanced by bothg → bbχ 0 1 and g → tb/tbχ ± 1 . Having identified in which region of parameter space of the pMSSM the radiative decay can dominate, we now turn on to which extent it can be constrained by existing ATLAS and CMS 8 TeV analyses.

Constraining the gluino loop decay from existing 8 TeV LHC analyses
It is expected that the typical signature of the radiative gluino decay will lead to a preponderance of jets. If favoured, when the mass difference ∆M = mg − mχ0 is small, the final state jets are typically as soft as those originating from the parton shower and in turn the gluino decay gets buried into the huge QCD background. To increase the sensitivity one can resort to, similarly to what is done concerning Dark Matter or compressed spectra searches, trigger on a hard initial-state-radiation (ISR) jet, the so-called monojet searches.
Since the radiative gluino decay has not been fully investigated at the LHC, we wish to fill this gap, using in particular monojet analyses to be sensitive to it. It is worth to note that the multijet analysis performed in [6] has indeed probed a small mass ∆M. Nevertheless, the interpretation has been done in a different context from ours, where the first and second generation squarks are not too heavy and therefore the three-body decay into light-flavour quarksg → qqχ 0 1 is not suppressed. Thus, one can probe small mass splitting between the gluino and the LSP in this case. In [6], the direct decay of the gluino to a gluon and a neutralino was also used to constrain mg and mχ0 1 , but based only on a fully hadronic search. Only numbers for particular values of mg and mχ0 1 were presented. For a massless neutralino, gluino masses below 1250 GeV can be excluded, and a lower mass limit of mχ0 1 = 550 GeV corresponding to mg = 850 GeV is quoted, but no full coverage of the mg − mχ0 1 mass plane has been presented. In [29], an exclusion contour in the mg − mχ0 1 mass plane has been derived using monojet searches, using the processg → qqχ 0 1 assuming 100% branching fraction, among other scenarios investigated. However, as we saw in the previous section, the dominance of this channel strongly depends on the squark spectrum, which is not detailed in [29], except that the stops and sbottoms are assumed to be light. We saw in the previous section that the radiative decay is favoured when light stops are present and therefore it is not clear if the assumption thatg → qqχ 0 1 dominates holds. In the context where the first and second generation of squarks are degenerate, bounds on their masses are pushed beyond the TeV scale. In the scenario we are focussing on, namely with decoupled first and second generations with somewhat lighter third generation, this effort is complementary to the official experimental analyses and worth to investigate. Achieving such a task then requires to recast the already existing ATLAS and CMS analyses since we do not have access to the raw data of both collaborations. The experimental signature for the gluino radiative decay is rather simple: it only consists of jets (possibly very soft) and missing transverse energy (MET). A characteristic feature of scenarios where the two-body radiative gluino decay dominate is typically the ones which are difficult to probe in a collider environment, namely ones where the mass difference between the mother and daughter particles is small (i.e compressed spectra). These scenarios are difficult to explore since they lead to final states with less energetic states or leptons, thus reducing the detection efficiency and signal acceptance. This may be part of the reasons why this decay pattern has not been fully considered as worth to investigate first in the past, as a priori its prospects are not very enthusiasming. In addition, in typical mSUGRA/CMSSM scenarios, this branching ratio is quite small since the mass splitting between the gluino of the LSP is generically quite large. However, the advent of monojet searches to precisely increase the sensitivity to compressed spectra has been a game changer in this respect. As noted in [43], when the ratio of the Higgs doublet vev's tan β ≃ O(1), a 125 GeV Higgs implies a non-negligible branching fraction of the radiative modes for the gluino decay. Moreover it is well-motivated in SUSY scenarios where the gluino is the next-to-lightest supersymmetric particle (NLSP), the socalled GNLSP models. Examining this process at the LHC can also put constraints on the viability of these models in solving the Dark Matter problem. Indeed, in such models, the right amount of relic density is obtained through important coannihilation processes between the LSP and the gluino and their efficiency is mainly driven by ∆M see for example, [87] and references therein. Hence, a full quantitative investigation of the radiative gluino at the LHC seems timely. The experimental signature of the radiative decay can be categorised in 1, 2 and 3 jets bins plus MET. Unfortunately there exists no published official analysis covering all such categories. In this purpose, and to cover all jet bins, we reimplemented within the MadAnalysis5 [83,84] framework the following three analyses: • ATLAS-SUSY-2013-21 [88]: this analysis targets the stop decay t 1 → c +χ 0 1 using a monojet analysis. It has also been used to probe the small squark-neutralino mass difference usingq → q +χ 0 1 , see [6], • ATLAS-SUSY-2013-02 [89]: search for squarks and gluinos in final states using high-p T jets with no leptons, 2-6 jets and large MET, • CMS-SUS-13-012 [90]: search for new physics in multijet events with large MET divided into three jet multiplicity categories (3-5, 6-7, and 8 jets), in order to work out the 8 TeV LHC constraints using 20.3 fb −1 of collected data. The recasted CMS-SUS-13-012 SUSY search was already available in the MadAnalysis5 Public Analysis Database [85] and can be found at [91]. The two remaining searches were implemented and validated for the present work and are now available at [92,93]. For the sake of clarity, we present in the Appendix A a comparison between the official cut flows and our reimplementations of the ATLAS monojet [88] and multijet [89] analyses within MadAnalysis5 (MA5). From Tables 4,7 and 8 the selection cuts of each respective analysis can be read off.
For the monojet search, see Table 4, one can see that the agreement is not very good at the level of the preselection cuts. The discrepancy originates already from the E miss T > 100 GeV cut applied at the reconstructed level. The MET trigger efficiency varies with E miss T and in particular is not 100% effective at E miss T = 100 GeV. To reproduce the MET trigger efficiency we parametrised the efficiency turn-on curve presented in [94] coming from the ATLAS simulation of the process pp → ZH → ννbb, as advised after communication with the ATLAS SUSY conveners. We already observe at this level a discrepancy which ranges from 16% to 32% for the three benchmark points between our implementation and the ATLAS result. Moreover we cannot reproduce the Trigger, Event Cleaning, and Bad Jet veto efficiencies, as we do not have access to this information in official documentation. However, once we enter the signal regions, the relative efficiencies of our cuts are comparable with the official ones and at the level of final number of events we observe an agreement between 15-25%, which is in the ballpark of expected accuracies from fast-simulation. More details about the validation of the recasting procedure can be found at [95]. For the ATLAS multijet analysis [89] a cut flow comparison is also presented in Tables 7 and 8. One can see that the agreement between the recasted analysis and the official is fairly good. The CMS multijet implementation and validation was already available on the PAD [85] before the initiation of this work and all details were presented there. As official results are not provided in terms of the gluino branching ratios and the radiative mode has not been fully investigated so far, we derived limits on this decay pattern within a Simplified Model approach. In the case we focussed only the gluino and LSP are relevant in the mass spectrum and we assume BR(g → gχ 0 1 ) = 100%. The signal generation was done using MADGRAPH5 [96,97] using the CTEQQ6L1 parton distribution functions [98], as where X = 0, 1 is the number of generated jets in the signal sample. The MADGRAPH samples are produced using the AUET2B tune [99, 100] 1 . The MLM [102] matching scheme is used, and a MADGRAPH k T measure cut-off and a PYTHIA [103] jet measure cut-off both set to 0.25 times the mass scale of the SUSY particles produced in the hard process. Hadronisation is performed using PYTHIA-6.426 [103] as incorporated in the MADGRAPH-5 package and detector effects are simulated with the 'MA5tune' of DELPHES-3 [104] as described in [84]. The number of events are then normalised to the correct luminosity after including cross sections at the next-to-leading order and next-to-leading logarithm accuracy [105], as tabulated by the LHC SUSY Cross Section Working Group [106] For the statistical interpretation, we make use of the module exclusion CLs.py provided in the MadAnalysis5 recasting tools. Given the number of signal, expected and observed background events, together with the background uncertainty (both directly taken from the experimental publications), exclusion CLs.py determines the most sensitive signal region (SR), the exclusion confidence level using the CL s prescription from the most sensitive SR, 1 It is worth to note that care should be taken when using recent versions of MadGraph5 together with the AUET2B tune. Indeed this tune was designed from a Leading-Order (LO) Matrix Element + Parton Shower (MEPS) merging. Since MadGraph5.2, the matching MEPS is done at next-to-leading order and in the same fashion as in MCNLO [101]. Therefore if one uses this tune together with a version 5.2 or higher of MadGraph, the interpretation of the results should be taken with great care. Indeed, we observed significant discrepancies in reproducing the official exclusion curves between using a recent version of MadGraph or the one actually adopted in the official analyses in [88,89]. That is why, for each analysis, we stick as much as possible to the Monte-Carlo configurations described in the experimental analyses. Thus, each signal sample has been generated with a different MadGraph version for each analysis we recasted. and the nominal cross section σ 95 that is excluded at 95% CL. The simplified model parameter space is simply scanned by varying mg and mχ0 1 until a 95% CL excluded number of BSM signal events is reached. The derived limits in the (mg, mχ0 1 ) plane are presented in Fig. 5. In the left panel of Fig. 5   mg < 2m t + mχ0 Tree Level σsum σNLO EW no QED Sommerfeld σNLO[10 −26 cm 3 s −1 ] Figure 5: Left panel: 95% CL exclusion contours for the radiative gluino decay simplified topology. The solid red line corresponds to the mass limits obtained from the MA5 recasted ATLAS monojet analysis [93], the red broken line from the MA5 recasted ATLAS multijet search [92] and the dashed-dotted line from the MA5 recasted CMS multijet analysis [91]. For comparison, the official 95% CL exclusion lines for theg → ttχ 0 1 SMS from ATLAS (green dashed line) [6] and CMS [23](blue dashed line) as well as for theg → qqχ 0 1 SMS from ATLAS [6](purple dashed line) are also shown. Right panel: 95% CL exclusion contours in the plane mg versus ∆M where ∆M = mg − mχ0 1 . Only the exclusion contours from the MA5 recasted monojet and multijet analyses are given since they provide the best sensitivity in the low ∆M region. analysis 2 . The results of the three recasted analyses (solid line : ATLAS monojet [93], broken line: ATLAS multijet [92] and dashed-dotted: CMS multijet [91]) are compared against three official published results: in green and blue are displayed the 95% CL limits obtained from the simplified topologyg → ttχ 0 1 from ATLAS [6] for the former and from CMS for the latter [23]. One immediately observes that the official SMS interpretations are limited when the tt threshold of the gluino three-body decay is closed. The CMS results pushes the limit a little bit above the tt threshold limit using off-shell tops, as compared to ATLAS. The purple broken line corresponds to the ATLAS limits in the (mg, mχ0 1 ) mass plane for theg → qqχ 0 1 simplified topology using the multijet search [6]. In the corresponding model investigated all squarks are decoupled and since the final states quarks are massless in this simplified approach, a small ∆M can be probed. In our scenario only the light-flavour squarks are completely decoupled from the low-energy spectrum and therefore our results are complementary to these. A word of caution is in order before discussing and interpreting our results. Indeed, we do not provide an estimation of the theoretical uncertainties on both the signal cross section and acceptance. This certainly limits our ability to provide an unambiguous statement on which portion of the parameter space in the (mg, mχ0 1 ) mass plane is excluded or not, but nevertheless provide a very interesting estimation of the sensitivity and mass reach of the 8 TeV analyses we reimplemented. Nevertheless, comparing with the existing literature enabled us to estimate the correctness of our results. First of all, comparing with Fig. 4 of [29], we see that the shape of the monojet exclusion curve is similar and its maximum (mg, mχ0 1 ) excluded values lie at (mg, mχ0 1 ) ≃ (700, 700) GeV, which is quite similar to our own maximum which sits at (mg, mχ0 1 ) ≃ (750, 750). In addition, the kink appearing for (mg, mχ0 1 ) ≃ (540, 400) GeV is also observed in other interpretations of monojet analyses (see [6,29]). The underlying explanation of the kink comes from the fact that the monojet analysis is not, strictly speaking, based on a single hard jet. Indeed, the monojet selection cuts in [88] actually allow a number of jets N jets ≤ 3 with p T > 30 GeV and |η| < 2.8. Thus the appearance of the kink is due to the fact that, starting from this point which possesses a sufficient ∆M, additional jets fulfilling the above requirement populate the SRs, thereby enhancing the sensitivity. Next, comparing with the numbers given in Fig. 21 in [6], for a massless neutralino, gluino masses up to mg = 1250 GeV are excluded, whereas we exclude up to mg = 1300 GeV (see the broken red line in the left panel of Fig. 5). A lower mass limit of mχ0 1 = 550 GeV for mg = 850 GeV is also quoted to be compared with mχ0 1 ≃ 600 GeV, mg = 850 GeV on our side. Therefore our results are in fairly good agreement with the existing litterature. Last, there has been numerous studies, mostly in the context of Simplified Dark Matter models (see e.g [107,108]), showing that the mono-jet searches can be sensitive to the decay width of the intermediate particles. However, since in our case the gluino decays through only one decay mode, its total width Γ is suppressed and Γ/mg ≪ 1, such that we can use safely the narrow-width approximation implicitly assumed in our SMS approach. Provided this important clarification, let us now discuss our results. As expected, the monojet analysis is the most sensitive search to probe the scenario where the gluino and neutralino are almost degenerate. Mass-degenerate gluino and LSP are excluded up to 750 GeV. As soon as ∆M increases, the efficiency of the monojet analysis quickly drops. This can be seen on the right panel of Fig. 5, where we display the two most sensitive recasted analyses in the small ∆M region. The colour coding is the same as in the left panel. The monojet analysis is the most effective in constraining a compressed gluino-neutralino spectrum up to ∆M ≃ 50 GeV. For larger ∆M the ATLAS multijet analysis becomes the most sensitive one in constraining the radiative decay. At low mg the signal region dubbed as 2jl ("2 loose jets ", more details about the SR definition can be found in the official analysis [89]) drives the exclusion curve, at moderate mg it is driven by SR 2jl and 3jm ("3 medium jets") and at large mg the 4jl ("4 loose jets") SR dominates. Within this analysis gluino masses up to mg ≃ 1300 GeV for a massless neutralino are excluded. It appears that the CMS multijet analysis is less powerful than the two ATLAS ones. There are two reasons for that, one is that the jet binning only starts from 3 jet bins and the second is that the search was designed as a discovery one, therefore its constraining power is less effective. Another comment is worth to be mentioned here: below the line where the tt threshold is open, interpreting the exclusion contour is highly debatable since we expect the three-body decays to take over. Therefore below this line our results should be taken with caution and the official results focussing on the three-body decayg → tt are more realistic. In the light of these results, it would be interesting to perform a combination of at least the two ATLAS analyses to get a more realistic exclusion curve. However, this goes beyond the scope of this paper since we do not have the necessary information at our disposal to perform the combination.

Prospects at the 13 TeV LHC
We address the discovery and exclusion reach of the radiative gluino decay at 13 TeV in this section. Since the radiative decay is dominant with a small mass gap betweeng and χ 0 1,2 , we design a special set of cuts optimized to investigate this case. To simplify matters we select benchmark points with ag − χ 0 1,2 SMS in mind, where the decayg → g χ 0 1,2 is 100 %. As we already observed in section 2, such an assumption is well motivated from theoretical considerations. We choose three representative benchmark points(BP) with nearly degenerate masses forg and χ 0 1 . To achieve this we decouple the rest of the spectrum from this set, i.e we set the three generation of squarks and the sleptons to 3 TeV. Since a higgsino like scenario is favourable for the radiative decay, we set M 1 , M 2 to 2 TeV, while µ is kept relatively light so that χ 0 1 , χ 0 2 are Higgsino like. For all benchmark points, the mass gap ∆m = mg −m χ 0 1 is fixed to around 10 GeV. The availability of phase space ensures that bothg → g χ 0 1 andg → g χ 0 2 are equally important. However, since χ 0 1 and χ 0 2 are almost degenerate, the decay products of χ 0 2 are soft, and are most likely to go undetected. The relevant masses and the branching ratios (BR) are tabulated in Table 1. The benchmark points were generated using SUSYHIT [86]. All the benchmark points satisfy the constraints derived in the previous section.  Table 1: The masses and branching ratios for the three benchmark points used for the collider analysis.
Since we focus on the nearly mass degenerateg− χ 0 1 scenario, the conventional search strategy is to look for a monojet + missing energy signature, where the hard ISR monojet recoils against the missing energy. However, at 13 TeV the number of QCD radiation jets from the gluino can be fairly large and carry large transverse momenta. We argue in this section, that a dijet + missing energy scenario (from ISR/FSR) is better suited compared to the traditional monojet + missing energy search strategy. We argue that the number of hard ISR jets can be significantly large at 13 TeV LHC, and including a second ISR jet helps considerably in improving the signal to background ratio. The principal backgrounds to this process are listed below, • QCD: The QCD dijet events are the largest source of backgrounds in terms of cross section (∼ 10 8 pb). A significant amount of missing energy is also likely to be present from detector mis-measurements.
• tt + jets: The multijet + missing energy topology is fairly common for all hadronic top decays. It is possible that the leptons and jets are missed which can lead to a dijet + missing energy topology. Since the tt + jets cross section is significantly large at 13 TeV (∼ 900 pb), even a small efficiency after cuts can result in a significantly large background cross section.
• Z + jets: This constitutes the irreducible part of the background when the Z boson decays invisibly to a pair of neutrinos. Since the cross section is quite large (∼ 10 5 pb), suppressing this background to a reasonable level is of primary requirement.
• ZZ: This background is similar to the Z + jets background, with one of the Z boson decaying hadronically while the other invisibly. This background is thus also one of the irreducible backgrounds for our case.
• W + jets: For a leptonic decay of W, a missed lepton would mean a topology similar to the signal. This has to be therefore considered as a serious background for this topology.
• WZ : The WZ background can be significantly large for a hadronically decaying W and an invisibly decaying Z.
Parton level events for the signal and background are generated using MADGRAPH5.0.7 [96], and passed on to PYTHIA6 [103] for showering and hadronisation. For the signal additional two partons are generated at the matrix element level. For backgrounds like tt + jets, W/Z + jets, additional 3 partons are generated in MADGRAPH5. The merging parameter for the matrix element-parton showering matching is set to 50 GeV. Since we anticipate that the bulk of the backgrounds are likely to originate from the tail of the p T spectrum we simulate W/Z + jets with a hadronic energy H T (defined as Σp j T ) cut of 400 GeV at the parton level in MADGRAPH5. The sample is then passed on to Delphes3 [104] (specifically the MadAnalysis5 tune [84] ) for detector simulation. Jets are reconstructed using Fastjet [109] with an antik T [110] algorithm and a p T threshold of 30 GeV and |η j | ≤ 3. Background cross sections are calculated using MADGRAPH5, while the gluino pair production cross section with decoupled sfermions are are quoted from the official SUSY cross section working group page [111]. We use the MadAnalysis5 [84] framework for the analysis of signal and background. The following cuts are applied to maximize the signal to background ratio: • Lepton Veto (C1): Since the signal has no leptons, a lepton veto is imposed. Leptons are selected with a with transverse momentum threshold, p l T ≥ 10 GeV and |η| ≤ 2.5. Leptons are isolated by demanding that the scalar sum of the transverse momenta of all visible stable particles within a cone ∆R = 0.2, does not exceed 10 % of p l T . This ensures that backgrounds with leptonic decays of W/Z are suppressed.
• Jets (C2): We demand exactly two jets in the final state. From the plot of number of jets (njets) for the signal and background (top left Fig. 6), we observe that even with a small mass gap for the signal, it is possible to obtain up to 3 jets quite easily from QCD radiation. The background, especially, for the W+ jets, peaks at 4 jets. Therefore it is convenient to design a search strategy with a dijet signature.
• b-jet veto (C3): To suppress the large tt background, we veto b-jets. This also ensures that backgrounds like Zbb, W bb are suppressed.
• p j 1 ,j 2 T > 600, 200 GeV (C4): From Fig. 6 we note that the leading ISR jet can be significantly energetic for the signal (top right, Fig. 6) and therefore we impose a hard cut on the transverse momenta of the leading jet. Although the second leading jet is not as energetic (bottom left, Fig. 6), the tail of the distribution can go up to about 400 GeV. We therefore impose a cut of 200 GeV on the second leading jet. The hard cuts on the leading jets ensure that we are in a region where the missing transverse energy that recoil against these hard ISR jets is high.
• M T 2 (C5): For this study, the variable M T 2 [112][113][114] is defined as, where the minimization is performed over all possible partitions of the missing transverse momentum, p / T = p / 1 T + p / 2 T , and j 1 , j 2 , represent the two leading jets. The transverse mass of the system is defined as The value of M T is bounded by the parent particle. It can be shown that this holds true for M T 2 as well, i.e, after minimization, M T 2 is bounded by the mass of the parent particle. To suppress SM backgrounds, where the only source of missing energy are the neutrinos, the value of the mass of the invisible particle is set to 0. SM backgrounds like WW, WZ, ZZ, tt, are expected to be cut off at the parent particle mass, while since the gluino is massive it is expected to go up to higher values. Uncorrelated/ISR jets however can significantly alter the shape of the M T 2 distribution [115]. For low mass differences, the extra ISR jets that dominate the jet configuration are not correlated with the p / T , and hence the M T 2 distribution extends well beyond the gluino mass. In the bottom left panel of Fig. 6 we present the M T 2 distribution for the signal(BP2) and the W/Z + jets background subject to all the previously imposed cuts. We observe that the M T 2 distribution falls sharply for the background, while the signal remains fairly flat. We use an optimized cut of 800 GeV to suppress the background.
We summarize our cut flows for signal and background in Table 2. For simplicity, we only document the backgrounds which leave a non negligible contribution after all cuts. In Table  2, the production cross section (C.S) for signal and background processes are tabulated in the third column in femtobarn. The number of simulated events (N) are noted in the 4th column. From the fifth column onwards the cumulative effect of cuts are presented. From  application of the M T 2 cut. Although the signal process suffers as well as a result of the M T 2 cut, the signal to background ratio is enhanced considerably. After all cuts, the total background cross section is reduced to 2.7 fb, while the signal cross sections vary from 1.6 fb for benchmark P1 to 0.21 fb in P3. In Table 3, we estimate the signal significance defined as S/ √ B by keeping the mass gap between the gluino and the lightest neutralino fixed at 10 GeV for the benchmark points. We estimate that one can observe a signal at 5 σ significance at 13 TeV with 30 fb −1 luminosity up to a gluino mass of 1 TeV while a gluino mass of 1.2 TeV can be excluded at the same luminosity. At 100 fb −1 luminosity the discovery reach goes up to 1.15 TeV, while we can exclude a gluino mass of up to 1.3 TeV. For the high luminosity run of LHC (3000 fb −1 ), we can discover a gluino mass up to 1. 45 TeV, excluding about 1.55 TeV. 3 We would like to compare our results with the standard monojet strategy at 13 TeV. However, since this is not available yet, a rough estimate could be obtained by a rescaling of the cross section from the 8 TeV result to the 13 TeV by assuming that the acceptance times efficiency remains the same. This has already been performed by the authors of [29] for the high luminosity LHC run (3000 fb −1 ). They predict that one can exclude a gluino mass of 1.25 TeV with a ∆M of 10 GeV, although in the context where BR(g → qqχ 0 1 ) = 100%. On this evidence the dijet + missing energy strategy devised here has a clear advantage, and we advocate the use of this strategy for 13 TeV LHC.

Conclusion
We have performed an investigation of the MSSM region where the gluino-neutralino spectrum is compressed and the loop-induced decayg → gχ 0 1 is dominant over three-body decays. For small gluino-neutralino mass differences ∆M, this decay mode is a sensitive probe of compressed spectra since it does not suffer from kinematical suppression factors. Within  the scenario we investigated, namely with decoupled heavy scalars but with third generation squarks closer to the electroweak scale, the loop-induced decay of the gluino into a pure higgsino-like neutralino dominates over other branching fractions until the tb threshold is crossed, when ∆M increases. This occurs whatever the hierarchy between the stops and the sbottoms, albeit larger branching fractions are reached when m b 1 ≫ m t 1 . On the contrary, the dominance of the radiative gluino decay into a bino-like neutralino or mixed bino-higgsino one over the other decay modes strongly depends on this hierarchy and other three-body decay modes start to be significant before the opening of the tb kinematical threshold. Adopting a Simplified Model approach, where the gluino and the neutralinoχ 0 1 are the only relevant superparticles accessible at the LHC, and BR(g → gχ 0 1 ) = 100%, we reinterpreted some ATLAS and CMS 8 TeV SUSY searches to derive 95% CL exclusion contours in the mg − mχ0 1 plane. This decay process is particularly interesting to probe small ∆M. The reinterpretation of the ATLAS and CMS analyses has been performed through the MadAnalysis5 framework [83,84] and publicly available on its Public Analysis Database web page [95]. The recasted monojet analysis enables us to illustrate that, had it been used by the experimental collaborations to constrain the loop-induced gluino decay, this search is sensitive to degenerate gluino-LSP scenarios. In turn, degenerate situations with gluino masses up to mg ≃ 750 GeV could have been excluded. This surpasses the official maximal value mg ≃ 600 GeV reached by the experimental collaborations using the processg → qqχ 0 1 . Then, concentrating on a pure di-jet search, we designed a dedicated search strategy to discover the gluino through theg → gχ 0 1 channel. For a mass gap fixed at ∆M = 10 GeV, a signal at 5 σ significance at 13 TeV with 30 fb −1 luminosity could be observed up to a gluino mass mg = 1 TeV, while the discovery reach goes up to 1.2 TeV. At 100 fb −1 luminosity the discovery reach goes up to 1.15 TeV, while we can exclude up to 1.3 TeV. A high-luminosity LHC could discover a gluino mass up to 1. 45 TeV while excluding about 1.55 TeV. In addition, our Monte-Carlo investigation indicated an interesting point. Indeed, a pure dijet search could be as sensitive as a monojet search and maybe even better. The underlying reason is related to the fact that a heavy gluino radiates a lot of high-p T ISR jets, even for small ∆M. Of course this has to be taken with a grain of salt since our investigation was performed only a the Monte-Carlo level and only a full detector simulation could give a clear cut answer, but this result is nevertheless worth to be pointed out. The discovery of a 125 GeV Higgs boson suggests that the scalar superpartners may lie in the multi-TeV range. Direct search of such heavy particles is impossible at the LHC. If the scalar mass scalem is much less thanm O(10 3 ) TeV, the gluino two-body decay is quite important in probing indirectlym. In the end, it may well be our only probe at our disposal in the case of SUSY scenarios with heavy scalars and compressed SUSY, if the gluino decays promptly in the detector. We hope our work will motivate the experimental collaborations to perform a dedicated analysis to search for this decay in order to make the most of the LHC potential.

A Cutflow for the ATLAS monojet analysis
We give below the cut flow table for the comparison between the ATLAS monojet analysis and the recasted MA5 one. The monojets analysis targets the flavour-violating decayt → cχ 0 1 with a branching fraction of 100% using a monojet and c-tagged strategies. We only recasted the monojet strategy. The dataset corresponds to 20.3 fb −1 of integrated luminosity at √ s = 8 TeV.  B Cutflow for the ATLAS multi-jet analysis This ATLAS analysis [89] searches for new physics in the 0 lepton + multi-jets (2-6 jets) + missing energy (E miss T ) final state. The dataset corresponds to 20.3 fb −1 of integrated luminosity at √ s = 8 TeV. In the context of supersymmetry, the analysis targets gluino pair production (gg), squark pair production (qq), and squark gluino production(qg). For each of the production modes the following cases are investigated;  Table 5: The benchmark scenarios used for the valiaion of the 10 signal regions. For the direct squark pair or gluino pair production, the rest of the spectrum is decoupled.
For squark-gluino production, the gluino and squark masses are assumed to be degenerate.
1200 1600 2200 700 1000 2200 Table 6: The signal region specific cuts. All energy units are in GeV.
For all of the above cases, all branching ratios are assumed to be 100 % and the rest of the spectrum is decoupled from this set. In the following tables we summarize the benchmark points used (Table 5), the cuts used for different signal regions(up to 4 jets, Table 6) , and finally the comparison between the ATLAS multi-jet analysis and the recasted MA5 one (Tables 7-8 Table 8: Cutflows for signal regions 4jl-,4jl and 4jt, compared to the official ATLAS results documented in [89].