Signals of a superlight gravitino at the LHC

Journal of High Energy Physics, Apr 2015

Abstract Very light gravitinos could be produced at a sizeable rate at colliders and have been searched for in the mono-photon or mono-jet plus missing momentum signature. Strategies for enhancing the signal over background and interpretations of the experimental results are typically obtained within an effective field theory approach where all SUSY particles except the gravitino are heavy and are not produced resonantly. We extend this approach to a simplified model that includes squarks and gluinos in the TeV range. In such a case, the jet(s)-plus-missing-momentum signature can be generated through three different concurring mechanisms: gravitino-pair production with an extra jet, associated gravitino production with a squark or a gluino, or squark/gluino pair production with their subsequent decay to a gravitino and a jet. By using a matrix-element parton-shower merging procedure, we take into account all the relevant production processes consistently, explore the SUSY parameter space with the LHC Run-I data set, and give prospects for the Run II. We also consider the reach of other signatures involving electroweak particles, e.g., the mono-photon, -Z, or -W plus missing momentum. The current mono-jet and mono-photon LHC analyses are interpreted to set a lower bound on the gravitino mass. We show how the limit of m3/2 > 1.7 × 10−13 GeV obtained in the effective field theory hypothesis is modified when the squarks and/or the gluino are in the TeV range.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP04%282015%29021.pdf

Signals of a superlight gravitino at the LHC

Received: February Signals of a superlight gravitino at the LHC Fabio Maltoni 0 1 2 Antony Martini 0 1 2 Kentarou Mawatari 0 1 Bettina Oexl 0 1 Open Access 0 1 c The Authors. 0 1 0 and International Solvay Institutes , Pleinlaan 2, B-1050 Brussels , Belgium 1 Universit e catholique de Louvain , Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve , Belgium 2 Centre for Cosmology , Particle Physics and Phenomenology (CP3) Very light gravitinos could be produced at a sizeable rate at colliders and have been searched for in the mono-photon or mono-jet plus missing momentum signature. Strategies for enhancing the signal over background and interpretations of the experimental results are typically obtained within an effective field theory approach where all SUSY particles except the gravitino are heavy and are not produced resonantly. We extend this approach to a simplified model that includes squarks and gluinos in the TeV range. In such a case, the jet(s)-plus-missing-momentum signature can be generated through three different concurring mechanisms: gravitino-pair production with an extra jet, associated gravitino production with a squark or a gluino, or squark/gluino pair production with their subsequent decay to a gravitino and a jet. By using a matrix-element parton-shower merging procedure, we take into account all the relevant production processes consistently, explore the SUSY parameter space with the LHC Run-I data set, and give prospects for the Run II. We also consider the reach of other signatures involving electroweak particles, e.g., the mono-photon, -Z, or -W plus missing momentum. The current mono-jet and mono-photon LHC analyses are interpreted to set a lower bound on the gravitino mass. We show how the limit of m3/2 > 1.7 1013 GeV obtained in the effective field theory hypothesis is modified when the squarks and/or the gluino are in the TeV range. Supersymmetry Phenomenology; Hadronic Colliders 1 Introduction Light gravitino production at the LHC SUSY QCD with a goldstino superfield Light gravitino production Gravitino pair production Associated gravitino production Indirect gravitino production Event simulation tools Mono-jet plus missing momentum Differential distributions Recasting LHC mono-jet analyses Merging matrix elements with parton showers Limit on the gravitino mass Mono-photon, -Z, or -W plus missing momentum Events with large missing momentum, and in particular those featuring just one visible recoiling object (a jet, a photon, a weak boson, a top quark), are among the most promising final states where to look for signs of new physics at colliders. Their simplicity and model independent nature appeal to both theorists and experimentalists. There are, however, important challenges that have to be faced with such signatures. The first ones are of experimental nature. The accurate and precise determination of the missing momentum in events needs a detailed control of many aspects, from triggering to jet energy scales, to underlying event simulation, to pile-up mitigation. In addition, in case of weak boson or top quark, tagging and reconstruction efficiencies for the recoiling object(s) also enter. The second class of challenges are more of theoretical nature and have to do with the problem of maximising the information that can be extracted from data to constrain new physics models. Model-independent searches for dark matter (DM) constitute the most popular interpretations of mono-jet analyses at the LHC, both in an effective field theory (EFT) framework as well as in simplified models, see e.g. [13] and the references therein. Among new complete physics scenarios leading to mono-object plus large missing momentum signals, supersymmetric (SUSY) models with a very light (or superlight) gravitino play a special role: they offer a concrete setting where the strengths and limitations of EFT approach vis-a-vis more UV completed models can be studied in detail. Let us look closer at model constraints from mono-object searches at previous and current colliders. At the LEP collider, the mono-photon signal was used to set a limit on models of SUSY with the gravitino as the lightest SUSY particle (LSP) and extra O(1014 9]. We dub such a scenario as gravitino EFT. The only relevant parameter in this case is the gravitino mass, which is directly related to the SUSY breaking scale, the lower limit the minimal supersymmetric standard model (MSSM) with other sparticles at the TeV scale. In this scenario, the process of the neutralino-gravitino associated production with the subsequent neutralino decay into a photon and a gravitino has been used to put a limit on the gravitino mass as a function of the neutralino and selectron masses [1116], e.g. considered as a simplified SUSY model, where only the gravitinos, the lightest neutralino and the selectrons play a role in the phenomenology at colliders. At the Tevatron, not only the mono-photon but also the mono-jet signals constrain models of SUSY [17, 18] and extra dimensions [1820]. Similar to the LEP bound, in the in the mono-jet [17] and mono-photon [18] channels, respectively. At the LHC, besides the mono-photon [22, 23] and mono-jet [24, 25] signals, other mono-object plus missing transverse momentum signals such as a Z boson [26], a lepton [27, 28], and a top quark [29] have been investigated mostly in the context of DM searches and more exotic models. SUSY models have been considered only in the ATLAS mono-jet analysis [24], where the gluino-gravitino [3035] and squark-gravitino [33, 34] associated productions were taken into account to set a limit on the gravitino mass as a function of the squark and gluino masses as, e.g. m3/2 > 1 1013 (4 1014) GeV relevant for this work is that the above limit may be modified by the contribution from the direct gravitino-pair production in association with an extra jet, a production channel so far disregarded in the analysis. Moreover, while event selection is targeted to the associated gravitino production, events from squark and gluino pair production may enter the signal region affecting the results. We would like to put forward the interpretation of the mono-object signals in the SUSY context with a very light gravitino for the LHC. As mentioned above, extending the gravitino EFT to the full MSSM (or simplified SUSY models), other production channels can contribute leading to rather different final state features that in turn depend on the SUSY parameters. In ref. [36] we studied the gluino-gravitino and gluino-pair production in this very same context. However, the gravitino-pair production associated with a jet and squark-gravitino production were not included there. In this work we present, for the first time, the complete set of production channels consistently treated in a unique framework that can provide accurate predictions for the general case. In addition, although the gravitino in our scenario is too light to be a cold DM candidate, the approach we have followed is fully general and can be used as a template for passing from an EFT approach to simplified models in the context of DM searches [37]. The plan of the paper is as follows. In section 2 we focus on the SUSY QCD sector in order to assess the parameter space relevant for gravitino production processes and potentially contributing to the mono-jet signature. We explicitly construct a SUSY QCD model in section 2.1. In section 2.2 we present the three different yet related mechanisms which produce gravitinos. Gravitino-pair production with one jet has been studied in the gravitino-EFT limit only [21], where exact tree-level results for 2 3 matrix elements for pp/pp GGj have been computed only for the quark-antiquark and quark-gluon initial states, but not for gluon-gluon ones. We obtain such results for generic squark/gluino masses and for all processes for the first time in this work. In section 2.3 we briefly review the computation/simulation tools used in this article. In section 3 we study all the relevant gravitino production processes in detail for total as well as differential cross sections. As an application of our results, we recast the ATLAS mono-jet analysis [24] with inclusive signal samples by merging matrix elements with parton showers (ME+PS) in order to set a limit on the masses of the SUSY particles. We suggest improvements to the analysis so to increase the sensitivity to the gravitino mass when squarks and gluinos are light. In section 4, we consider the associated production with an electroweak (EW) particle, and study the mono-photon, -Z and -W signals in the very light gravitino context. Finally, we recast the mono-photon analyses at the LHC [22, 23] to set a limit on the gravitino mass. Section 5 is devoted to our conclusions. Light gravitino production at the LHC In this section we start by constructing a SUSY QCD model by using the superspace formalism. We then present the three mechanisms of light gravitino production at hadron colliders and finally we briefly describe the simulation tools we employ for our results. SUSY QCD with a goldstino superfield In phenomenologically viable SUSY models, SUSY breaking is often assumed to take place in a so-called hidden sector, and then transmitted to the visible sector (i.e. the SM particles and their superpartners) through some mediation mechanism, e.g. gauge mediation or gravity mediation. As a result, one obtains effective couplings of the fields in the visible sector to the goldstino multiplet. To illustrate the interactions among the physical degrees of freedom of the goldstino multiplet and the fields in the visible sector, we introduce an where the color and generation indices are suppressed. In addition, we introduce a chiral DV , FL/R and FX are auxiliary fields. The Lagrangian of the visible sector is Lvis = 1 Z where gs is the strong coupling constant.1 1 D D e2gsV D e2gsV denotes the SUSY SU(3)C field strength tensor with D being the superderivative. Lvis contains the kinetic terms as well as the gauge interactions. The Lagrangian of the goldstino part is given by LX = 4 The first term gives the kinetic term of the sgoldstino and the goldstino, while the second 2 The last term is non-renormalizable and provides interactions in the goldstino multiplet. In addition, this term also gives the sgoldstino mass term when replacing the The effective Lagrangian that leads to the interactions among the (s)goldstinos and the fields in the visible sector as well as the soft mass terms for the squarks and the gluinos is given by Lint = enough to generate all the relevant interactions involving two goldstinos in the final state for the jet(s)+E/ T signal at hadron colliders. The extension of the model including the SM Let us briefly refer to the goldstino equivalence theorem. When the global SUSY is Higgs mechanism. In the high-energy limit, promoted to the local one, the goldstino is absorbed by the gravitino via the so-called superm3/2, the interactions of the helicity 1/2 components are dominant, and can be well described by the goldstino interactions due to the gravitino-goldstino equivalence theorem [39, 40]. As a consequence of the super-Higgs mechanism, the gravitino mass is related to the SUSY breaking scale and the Planck mass as [41, 42] m3/2 = 3 M Pl G G pair (red), gluino-gravitino (blue) and gluino-pair (green) diagrams are sorted. The diagrams are ordered with the number of additional QCD partons in rows, while with the total parton multiplicity SUSY breaking scenarios such as GMSB provide a gravitino LSP. In the following, we simply call the goldstino gravitino. Light gravitino production Given the model we constructed in the previous section, we now consider light-gravitino production in R-parity conserving scenarios that lead to jet(s) plus missing momentum at pp jet(s) + E/ T , where the missing momentum is carried by two LSP gravitinos. At the leading order in QCD, the relevant processes are: 1. gravitino-pair production in association with a quark/gluon emission from initial state radiation, a gravitino and a quark/gluon, 2. gravitino production associated with a squark/gluino with the subsequent decay into 3. SUSY QCD pair production with the subsequent decay into gravitino and a The processes are schematically represented in figure 1. The processes in the second column of figure 1 contribute in an obvious way to the mono-jet signal. However, also the 2-parton final states will contribute either in the exclusive 1-jet analysis because one parton might not give rise to a jet or when the analysis is fully or in part inclusive over other jets. In the current ATLAS and CMS mono-jet analyses [24, 25], for example, a second jet is allowed signals, we simply replace the QCD processes by the EW processes, i.e. replace gluinos by neutralinos and charginos. We now consider each production channel in more detail. Gravitino pair production Direct gravitino-pair production at colliders has been studied only in models where all SUSY particles except for the gravitino are too heavy to be produced on-shell, i.e. in the gravitino EFT limit [8, 9, 21]. One of the aims of this article is to extend the previous studies to take into account the effect of other SUSY particles in spectrum. This has been done recently for mono-photon signals at future linear colliders [43], and we now apply for it to the QCD sector for the LHC. A pair of gravitinos is produced through both the qq and gg initial states, Another feature is that the cross section tends to be larger for heavier squarks and gluinos, which are propagating in the t and u channels. For the gg channel, there are diagrams featuring s-channel sgoldstino. These play an important role in the computation of cross sections even when sgoldstinos are too heavy to be produced; see ref. [43] for more details. As expected from the colourless nature of the gravitinos, an extra parton in the final state mainly comes from initial state radiation and therefore it is naturally suppressed by (or equivalently from the minimum missing momentum). We will investigate those effects carefully in section 3. The 2 3 processes pp(qq, qg, gg) GGj, and can be observed if extra radiation is hard enough to be detected, for instance in the form of one or more jets. The helicity amplitudes for the above 2 2 processes were production channel is that the corresponding total cross section scales as the inverse of the gravitino mass to the fourth power, pp(qq, gg) GG, have been calculated for qq and qg initial states in the gravitino EFT limit, yet the gg process was estimated only by the 2 2 cross section in the limit of the soft and collinear gluon radiation [21]. In this article, as shown later, we consider all the amplitudes at tree-level without any approximation and calculate the full matrix elements numerically. Associated gravitino production Gravitino production in association with a squark or a gluino and the subsequent decay into a gravitino and a quark/gluon, pp qG, gG GGj, pp qq, qg, gg GGjj. As mentioned above, in the current mono-jet analyses by ATLAS [24] and CMS [25], events with a second jet have been included as the signal typically contains more jets from QCD radiation. Therefore, depending on cuts, the jets coming from the decay of heavy SUSY particles may contribute to the signal region. We also note that, when the gravitino is very light, the t-channel gravitino exchange enhances the cross sections [3033]. Before turning to the collider phenomenology part, it may be worth to mention the decay width of the squark and gluino. The partial decay width of a squark (gluino) into a quark (gluon) and a gravitino is given by and hence the dependence of the gravitino mass is milder than in the gravitino-pair production. Similar to the GG production, heavier squarks and gluinos in the t and u channels enhance the cross sections, while those in the final state suppress the cross sections due to the phase space. 2.2.3 Indirect gravitino production SUSY QCD pair productions, i.e. squark-pair, gluino-pair and squark-gluino productions, have been systematically studied, motivated by the inclusive SUSY searches as well as in simplified SUSY searches. On the other hand, they have not been considered in the monojet analysis since more than one jet in the final state is expected. Especially, when squarks and/or gluinos are the next-to-lightest SUSY particle (NLSP), their decay can provide the di-jet plus missing momentum signal at the LO [44, 45]: leads to the j + E/ T signal at the leading order (LO), and has been studied in [3035]. The tree-level ME+PS merging technique has also been applied for this process in [36]. Unlike the gravitino-pair production in eq. (2.7), the cross section is inversely proportional to the square of the gravitino mass, where the gravitino mass in the phase space is neglected. When the gravitino is very light and/or the squarks and gluinos are heavy, the width of the squark and gluino can be a significant fraction of the mass. At the same time, the gravitino couplings become strong and the perturbative calculations are not reliable. To identify a reasonable SUSY (blue), and mq < mg (black).3 We assume all other SUSY particles are heavier than the squarks and the gluino. For the mq > mg case, the additional q g + q decay channel is opened. For the mq < mg case, on the other hand, the gluino has all possible squark decay modes, and hence its width becomes significantly larger than the squark one, strongly depending on the mass difference. In the following, a benchmark scenario will be identified 3The widths are obtained numerically by the decay package MadWidth [46]. x =0.25 x =0.5 Event simulation tools Here, we briefly describe event simulation tools we employ in this article. We follow the strategy presented in ref. [47] to new physics simulations. Similar to the SUSY QED model of ref. [43], we have implemented the SUSY QCD Lagrangian with a goldstino supermultiplet described in section 2.1 into FeynRules2 [38], which provides the Feynman rules in terms of the physical component fields and the UFO model file [48, 49] for matrix-element generators such as MadGraph5 aMC@NLO [50]. In this work, instead of employing a dedicated implementation of the four-fermion vertices involving more than one Majorana particle [43], we introduce auxiliary heavy particles for the multi-jet simulation. Parton-level events generated by MadGraph5 aMC@NLO are passed to Pythia6.4 [51] for parton shower and hadronisation, to Delphes3 [52] for detector simulation, and to MadAnalysis5 [53] for sample analyses. Mono-jet plus missing momentum In this section, we first present total and differential cross sections to illustrate how the three gravitino production processes depend on the SUSY mass parameters. Then, we recast the ATLAS mono-jet analysis [24] to constrain the gravitino mass in cases that go beyond the gravitino-EFT scenario. In the following, we consider three scenarios where squark and/or gluino masses are O(10) TeV and O(1) TeV: mq = mg = 20 TeV (the gravitino-EFT limit), mq = 20 TeV, mg = 1 TeV (the heavy-squark limit), mq = mg = 1 TeV, A: mq~= mg~= 20 TeV B: mq~= 20 TeV,mg~= 1 TeV s = 8 TeV as a function of the gravitino mass for case A (left) and B (right). For the gravitino-pair production while we keep the sgoldstino masses at 20 TeV. For simplicity, we assume that all the noncolored SUSY particles are heavier than the colored ones, and hence the decay mode of squarks and gluinos is only into gravitinos. Only the gravitino-pair production contributes to the signal for case A, while the gG and gg productions can also give the signal for case B. In case C all the subprocesses can be comparable. We note that the masses ref. [21], where all the SUSY particles except gravitinos are integrated out, i.e. where the computation has been done in the gravitino-EFT limit. for the three scenarios at Figures 3 and 4 (left) show the total cross sections as a function of the gravitino mass QCD emission (GG + j), we impose a minimal transverse momentum cut for the jet with with the factorization and renormalization scales at pjT for the gravitino-pair production, mq,g for the SUSY QCD pair production. We note that all our results are the LO predictions although it is well known that higher-order QCD corrections are large. For example, LHC [55, 56], while the higher-order calculations have not yet been done for the gravitinopair production and the associated gravitino production. Our analyses can be redone with different overall normalizations and yet the main features will not change. cesses, respectively, as discussed in section 2.2. For the SUSY QCD pair productions, C: mq~= mg~= 1 TeV m3/2 = 210-13 GeV qq/qg/gg, the contribution of the t-channel gravitino exchange can be visible if the gravitino is lighter than about 3 1013 GeV. We also show the total rates as a function of the degenerate squark and gluino masses production, the cross section increases as the squarks and gluinos become heavier. On the other hand, the cross sections for the associated production and the SUSY QCD pair production decreases due to the phase space suppression. As can be seen in figures 3 and 4, each contribution to the total rates strongly depends on the SUSY mass parameters, and the different contributions can be comparable for certain parameters. However, the resulting signature can be still distinctive among the subprocesses as shown below. Differential distributions We now consider differential distributions for the direct gravitino-pair production in detail. This is the first presented result that goes beyond the gravitino EFT limit. Figure 5 shows normalized missing transverse momentum distributions for the three benchmark scenarios in (3.1). Here parton-shower and detector effects are included, and the detector cut E/ T > 120 GeV are applied. Jets are reconstructed employing the anti-kT algorithm [57] with a radius parameter of 0.4. Depending on the mass of the t-channel exchanged squarks and gluinos, the contributions from different initial states can be of different relevance. Moreover, the energy spectra from qq and gg are similar, while that from qg is harder than Figure 6 presents several kinematical distributions of all the production channels for case C as well as the SM Z + j background. We stress that the purpose of including the 200 400Emiss [GeV] 600 T tion with an extra radiation for the three benchmarks in (3.1) at the LHC-8TeV. Parton-shower and detector effects are included for the event generation and a cut E/ T > 120 GeV is imposed. The contributions from different initial states are also shown. Z + j background is illustrative on the one hand and to provide a normalisation point for experimentalists. Needless to say, many other important sources of backgrounds need to be included for a complete analysis, such as those coming from W +jets or just (mis-measured) jets. Most of them, however, can only be meaningfully estimated in presence of a detailed detector simulation and data validation. We see that the SUSY signals are harder than the SM background, even for the gravitino-pair production. This is mainly due to the 2 3 kinematics of the signal, whereas the background essentially has the 2 2 kinematics. Besides the background, GG(+j) has the softest spectra, while qq/qg/gg lead the hardest. The differences in the pT spectrum of the second-leading jet are rather significant. The second jet mostly comes from the squark or gluino decay for the SUSY QCD pair production, while mainly from QCD radiation in the gravitino-pair and associated productions. We note that the shapes for the available subprocesses are very similar among the three scenarios in (3.1), while the rates are different as seen in the previous subsection. Recasting LHC mono-jet analyses ATLAS and CMS have reported a search for new physics in mono-jet plus missing transverse momentum final states. The null results are translated into limits on a gauge-mediated SUSY, large extra dimension and dark matter models in ATLAS [24] and on dark matter, large extra dimension and unparticle models in CMS [25]. As mentioned in the introduction, in the ATLAS analysis, a light gravitino scenario has been studied, but only the squark-gravitino and gluino-gravitino associated productions. In this section, taking into account all the possible gravitino production processes described above, we recast the ATdifferent squark and gluino masses. C: mq~ = mg~ = 1 TeV C: mq~ = mg~ = 1 TeV C: mq~ = mg~ = 1 TeV C: mq~ = mg~ = 1 TeV Selection cuts The event selection of the ATLAS analysis [24] is E/ T > 120 GeV, at most two jets with p E/ T > 120 GeV + at most 2 jets SR1 +E/ T > 250 GeV SR2 +E/ T > 350 GeV the number of events passing each step of the selection requirements in (3.2) and (3.3), expected as a reference. The third requirement allows the second-leading jet (j2) since signal events typically contain jets from initial state radiation, while the last one reduces the QCD background where the large E/ T originates from the mis-measurement of pjT2 . On top of the above requirements, similarly to the ATLAS analysis, we define three signal regions (SRs) with different E/ T In table 1 we present SUSY signal predictions for the number of events passing each step of the above selection requirements. As in figure 6, we generate events for each subprocess including parton-shower and detector effects. In addition to the three SUSY table 2 in the ATLAS analysis [24] for more details on the background estimation including parton shower, the relation does not hold any more, and the effect of the radiation is quite large for the gravitino pair production. As expected, the third selection cut in (3.2) does not affect so much for GG(+j) and qG/gG, while significantly reduces the SUSY QCD pair contributions although for case C the contribution is still substantial and even dominant in SR3. We remind the reader that SUSY QCD pair production is insensitive to the gravitino 4SR2 in the ATLAS analysis is with the 220 GeV cut [24]. On the other hand, our SR2 is similar to the one of the signal regions in the CMS analysis [25]. m3/2 = 21013GeV LHC-8TeV (10.5 fb-1) B: mq~= 20 TeV,m~= 1 TeV m3/2 = 21013GgeV m3/2 = 21013GeV compared with the merged samples containing an extra parton (solid). Only the cut E/ T > 120 GeV be considered as background to constrain the gravitino mass. To reduce this SUSY QCD background, on top of the above signal selection cuts, we impose a maximal pT cut on the second-leading jet in each SR as denoted as SR1, SR2 and SR3. As can be also seen in the pjT2 distribution in figure 6, this cut removes the large part of the events coming from qq, qg and gg. Merging matrix elements with parton showers So far, in order to identify characteristics and differences among them we have treated each gravitino-production subprocess independently. Now, to constrain the SUSY mass parameters, we generate inclusive signal samples by using the ME+PS merging procedure. In practice, following ref. [36], we make use of the shower-kT scheme [58], and generate signal events with parton multiplicity from one to two, pp GG +1, 2 partons, and merging variation of Qcut did not change the distributions after the minimal missing transverse energy cut E/ T > 120 GeV. The factorization and renormalization scales are set to the scalar sum of the pT of all the partons in the final state. We note that the employment of the ME+PS merging procedure allows us to treat different contributing processes, i.e. gravitinopair, associated gravitino and SUSY QCD pair productions (see also figure 1), within one event simulation and without double counting. We also note that the interference among the different production processes is very small since the width of the on-shell squarks and gluinos is small with our parameter choice. To see the effect of an extra parton in the matrix element, in figure 7 we compare the inclusive samples of the GG + 1 parton in the matrix element with the merged samples of pp GG + 1, 2 partons. For case A, where only the gravitino-pair production contributes, we find a slightly harder spectrum in the high E/ T region for the merged sample due to the second parton in the matrix element. For case B, as seen in table 1, besides GG, A: mq~= mg~= 20 TeV LHC-8TeV 95% CL limit (SR1) SR B: mq~= 20 TeV,mg~= 1 TeV C: mq~= mg~= 1 TeV (dashed) at s = 8 TeV. s = 8 TeV (solid) and 13 TeV (dotted) as a function of the gravitino mass, where SR1 and SR3 are shown. The predictions are compared with the model-independent 95% confidence level (CL) upper limits by the ATLAS analysis [24]. Right: same as the left panel, but for all the three scenarios in SR3 (solid) and SR3 the gG production contributes significantly, leading to a much harder spectrum than in case A. Again, a harder spectrum for the merged sample is observed as expected. For case C, with the minimal selection cut E/ T > 120 GeV, the SUSY QCD pair productions, especially qq and qg, are dominant, which do not exist in the GG + 1 parton sample. Therefore, the distributions are completely different without and with an extra parton in the matrix-element level. Limit on the gravitino mass By using the inclusive ME+PS merged samples, we can now recast the ATLAS-8TeV confidence level (CL) upper limit on the visible cross section, defined as the production values are 2.8 103 fb and 50 fb for SR1 and SR3 selections, respectively. s = 8 and 13 TeV as a function of the gravitino mass. The horizontal lines show the ATLAS 95% CL limits. In SR1 the SM background is huge, and hence only the very light gravitino case can be constrained. The constraint in SR3 is slightly better than in SR1, and the gravitino mass order of magnitude stronger than the limits at the LEP and Tevatron [10]. According to the relation in (2.4), the above limit corresponds to the SUSY breaking scale of about 850 GeV. The coming LHC Run-II with s = 8 TeV are shown for expected. For case C, on the other hand, no sensitivity of the cross section to the gravitino G G G emission (left) and neutralino-gravitino associated production (right) contribute. by imposing an additional cut on the second-leading jet in (3.4), the sensitivity to the gravitino mass recovers even for heavier gravitinos since the SUSY QCD pair productions are strongly suppressed. The maximal pjT2 cut hardly affects the signals for case A and B. Mono-photon, -Z, or -W plus missing momentum In an analogous way to the mono-jet signal discussed in the previous section, superlight mentum signature via 2. gravitino production associated with a neutralino/chargino with the subsequent decay The schematic diagrams are shown in figure 9. Unlike the j + E/ T signal, only the qq initial state can contribute to the mono-EW boson+E/ T signal. In this section, for simplicity, we consider the heavy neutralino/chargino limit, where only the gravitino-pair production contributes.5 done independently, but the combined analysis may be very interesting because there is a possibility to determine left-right handedness of the new physics interactions. Instead of studying the gravitino-mass constraint in each search channel, figure 10 shows the ratio of diagrams, and for illustration we take three left- and right-handed squark mass scenarios: (mqL , mqR ) = {(20, 20), (20, 1), (1, 20)} TeV. The effect of the mass of the gauge boson can be seen as suppression and enhancement in the low and high pT region, respectively. Interestingly, the ratios are very sensitive to the mass difference between qL and qR, especially for the W boson, which only couples to the left-handed squarks. Finally, we recast the LHC-8TeV mono-photon analyses [22, 23], where non-SUSY models were studied, to constrain the gravitino mass. For event selection, we follow the m3/2 = 11013GeV (m~qL, m~qR) = photon for pp GGV (V = , Z, W ) at for different left- and right-handed squark masses are considered. s = 8 TeV with m3/2 = 1 1013 GeV. Three scenarios The photon and the missing momentum vector are also required to be well separated Possible jets produced by ISR are defined by the anti-kT algowith pT > 30 GeV. While events with more than one jet are rejected, events with one As discussed in the mono-jet signal, the cross section for the gravitino-pair production s = 8 TeV, becomes larger as the t-channel squark masses increase. In analogy with the mono-jet case, the SUSY signal is harder than the SM background mainly due to the kinematics. also on the kinematical cuts. The ATLAS + E/ T study with 20.3 fb1 of collisions at s = 8 TeV reported a s = 8 and 13 TeV as a function of the gravitino mass for three different squark masses. The horizontal line shows the ATLAS 95% CL limit, where we take a conservative estimate for the fiducial mq~ = 20 TeV 2 TeV 1 TeV s = 8 TeV with SUSY mass limit, which is translated to the lower bound on the SUSY breaking scale of about 850 GeV, similar to the mono-jet limit. For lighter squark masses the limits are lower, for example, m3/2 8.4 1014 GeV, i.e. F 600 GeV for 1-TeV squarks. These results significantly improve previous ones at LEP and the Tevatron, and are comparable with the recent ATLAS 8-TeV mono-jet analysis [24].6 The coming LHC Run-II with of the SUSY breaking scale. We note that we assumed the heavy neutralino limit in this section. However, if the neutralino is light enough and promptly decays, production of the on-shell neutralino can give rise to characteristic harder photons. This leads to different for the mono-jet study in the previous section can be applied for the mono-photon case by the replacement of gluino/gluon to neutralino/photon for the qq initial state. The mono-jet plus missing momentum signal at the LHC is a promising final state where to look for new physics. In this work we investigated the possibility of observing a SUSY signal via a very light gravitino. Gravitino-pair production with extra radiation and associated gravitino production with a squark or a gluino contribute both to mono-jet signals. Moreover, in the current ATLAS and CMS mono-jet analyses, squark and gluino pair production may contribute to the signal region. We have carefully investigated the impact of consistently including all three production channels. We have constructed a SUSY 6In the ATLAS study, only associated gravitino production with a gluino or a squark was considered. q~= 8 TeV 13 TeV 1 s = 8 TeV (solid) and 13 TeV (dotted) as a function of the gravitino mass for different squark masses. The predictions are compared with the model-independent 95% confidence level (CL) upper limit by the ATLAS analysis [23]. QCD model, lifting previous limitations of gravitino-EFT models. We have implemented it in the FeynRules and MadGraph5 aMC@NLO simulation framework paying special attention to needed Majorana four-fermion interactions. We discussed the parameter dependence of the signal rate in detail and showed that the relative importance of the three contributing subprocesses varies with the gravitino and SUSY particle masses. We also studied the differential distributions to get better understanding of the expected shape for different parameters. To constrain the gravitino and other SUSY masses we have recast the LHC-8TeV monojet analyses by the ATLAS and CMS collaborations. Using matrix-element/parton-shower merged samples, we have been able to treat all three contributing subprocesses within one event simulation and without double counting. Re-interpreting the reported modelindependent 95% CL upper limit on the visible cross section, we found that a gravitino the gravitino are very heavy. We showed that this limit changes when allowing squarks and gluinos to be relatively light. To get a better sensitivity to the gravitino mass, we suggest an additional cut in the analysis which suppresses contributions from SUSY QCD pair production. We have also discussed prospects for the LHC Run-II, which is expected to explore gravitino masses up to O(1012) GeV. Finally, we also considered production of EW particles and investigated the monophoton, -Z and -W plus missing momentum signals. We have performed a detailed analysis for gravitino-pair production, showing that the ratios of the different vector bosons in the final state might reveal information about left- and right-handed couplings. reinterpreted the mono-photon analysis at s = 8 TeV, and found a similar limit as in the mono-jet analysis in the case where all SUSY particles except the gravitino are very heavy. For lighter squark masses, the limits are lower. We have concluded by presenting the outlook for the LHC Run-II. Acknowledgments This work has been performed in the framework of the ERC grant 291377 LHCtheory: Theoretical predictions and analyses of LHC physics: advancing the precision frontier and of the FP7 Marie Curie Initial Training Network MCnetITN (PITN-GA-2012-315877). It is also supported in part by the Belgian Federal Science Policy Office through the Interuniversity Attraction Pole P7/37. The work of AM and FM is supported by the IISN MadGraph convention 4.4511.10 and the IISN Fundamental interactions convention Energy Physics and the Research Council of the Vrije Universiteit Brussel. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [arXiv:1308.2679] [INSPIRE]. LHC, arXiv:1409.2893 [INSPIRE]. direct detection experiments, arXiv:1409.4075 [INSPIRE]. [3] S. Malik et al., Interplay and characterization of dark matter searches at colliders and in collisions at collisions at collisions at s up to 209 GeV, Eur. Phys. J. C 28 (2003) 1 [INSPIRE]. [8] O. Nachtmann, A. Reiter and M. Wirbel, Single jet and single photon production in 27 (1985) 577 [INSPIRE]. (1999) 653] [hep-ph/9711516] [INSPIRE]. Phys. C 38 (2014) 090001. Phys. Lett. B 175 (1986) 471 [INSPIRE]. Lett. B 258 (1991) 231 [INSPIRE]. Phys. Rev. Lett. 77 (1996) 5168 [hep-ph/9609524] [INSPIRE]. [hep-ph/9611437] [INSPIRE]. large missing transverse energy in pp collisions at 1378 [hep-ex/0003026] [INSPIRE]. s = 1.8 TeV, Phys. Rev. Lett. 85 (2000) Rev. Lett. 89 (2002) 281801 [hep-ex/0205057] [INSPIRE]. plus missing energy final states at [arXiv:0803.2137] [INSPIRE]. s = 1.8 TeV, Phys. [19] D0 collaboration, V.M. Abazov et al., Search for large extra dimensions via single photon [20] CDF collaboration, T. Aaltonen et al., Search for large extra dimensions in final states containing one photon or jet and large missing transverse energy produced in pp collisions at hadron colliders when the other superparticles are heavy, Nucl. Phys. B 526 (1998) 136 [Erratum ibid. B 582 (2000) 759-761] [hep-ph/9801329] [INSPIRE]. [22] CMS collaboration, Search for new phenomena in monophoton final states in proton-proton [23] ATLAS collaboration, Search for new phenomena in events with a photon and missing collisions at s = 8 TeV, arXiv:1410.8812 [INSPIRE]. transverse momentum in pp collisions at D 91 (2015) 012008 [arXiv:1411.1559] [INSPIRE]. momentum final states using 10 fb1 of pp collisions at at the LHC, ATLAS-CONF-2012-147 (2012). [24] ATLAS collaboration, Search for new phenomena in monojet plus missing transverse s = 8 TeV with the ATLAS detector events in proton-proton collisions at s = 8 TeV, arXiv:1408.3583 [INSPIRE]. [25] CMS collaboration, Search for dark matter, extra dimensions and unparticles in monojet [26] ATLAS collaboration, Search for dark matter in events with a Z boson and missing [27] ATLAS collaboration, Search for new particles in events with one lepton and missing transverse momentum in pp collisions at D 90 (2014) 012004 [arXiv:1404.0051] [INSPIRE]. transverse momentum in pp collisions at (2014) 037 [arXiv:1407.7494] [INSPIRE]. s = 8 TeV with the ATLAS detector, JHEP 09 [28] CMS collaboration, Search for physics beyond the standard model in final states with a s = 8 TeV, arXiv:1408.2745 [INSPIRE]. D 41 (1990) 2347 [INSPIRE]. C90-10-04 (1990). [29] CMS collaboration, Search for monotop signatures in proton-proton collisions at production at hadron colliders, Phys. Rev. D 57 (1998) 373 [hep-ph/9707331] [INSPIRE]. and LHC perspectives, Phys. Rev. D 75 (2007) 115003 [hep-ph/0610160] [INSPIRE]. association with gluinos at the LHC, JHEP 10 (2012) 008 [arXiv:1206.7098] [INSPIRE]. models, JHEP 11 (2014) 024 [arXiv:1402.2285] [INSPIRE]. high-energy equivalence theorem, Phys. Lett. B 215 (1988) 313 [INSPIRE]. theorem in spontaneously broken supergravity, Phys. Rev. D 39 (1989) 2281 [INSPIRE]. 18 (1973) 312 [INSPIRE]. 1433 [INSPIRE]. colliders, Eur. Phys. J. C 74 (2014) 2909 [arXiv:1402.3223] [INSPIRE]. [45] Y. Kats, P. Meade, M. Reece and D. Shih, The status of GMSB after 1/fb at the LHC, JHEP 02 (2012) 115 [arXiv:1110.6444] [INSPIRE]. MadGraph5/aMC@NLO, arXiv:1402.1178 [INSPIRE]. [46] J. Alwall et al., Computing decay rates for new physics theories with FeynRules and C 71 (2011) 1541 [arXiv:0906.2474] [INSPIRE]. (2012) 1201 [arXiv:1108.2040] [INSPIRE]. Libraries Of Helicity Amplitudes for Feynman diagram computations, Comput. Phys. 079 [arXiv:1405.0301] [INSPIRE]. (2006) 026 [hep-ph/0603175] [INSPIRE]. [1] A. DiFranzo , K.I. Nagao , A. Rajaraman and T.M.P. Tait , Simplified models for dark matter interacting with quarks , JHEP 11 ( 2013 ) 014 [Erratum ibid . 1401 ( 2014 ) 162] [2] J. Abdallah et al., Simplified models for dark matter and missing energy searches at the [6] L3 collaboration, P. Achard et al ., Single photon and multiphoton events with missing energy [9] A. Brignole , F. Feruglio and F. Zwirner , Signals of a superlight gravitino at e+e colliders when the other superparticles are heavy, Nucl . Phys . B 516 ( 1998 ) 13 [Erratum ibid . B 555 [10] Particle Data Group collaboration , K. Olive et al., Review of particle physics, Chin. [11] P. Fayet , Lower limit on the mass of a light gravitino from e+e annihilation experiments , [14] J.L. Lopez , D.V. Nanopoulos and A. Zichichi , Single photon signals at LEP in supersymmetric models with a light gravitino , Phys. Rev. D 55 (1997) 5813 [15] S. Baek , S.C. Park and J.-h. Song, Kaluza-Klein gravitino production with a single photon at [16] K. Mawatari , B. Oexl and Y. Takaesu , Associated production of light gravitinos in e+e and [17] CDF collaboration, T. Affolder et al., Limits on gravitino production and new processes with [21] A. Brignole , F. Feruglio , M.L. Mangano and F. Zwirner , Signals of a superlight gravitino at [30] D.A. Dicus , S. Nandi and J. Woodside , Collider signals of a superlight gravitino , Phys. Rev. [31] M. Drees and J. Woodside , Signals for a superlight gravitino at the LHC , IS-J- 4137 , [32] D.A. Dicus and S. Nandi , New collider bound on light gravitino mass , Phys. Rev. D 56 [33] J. Kim , J.L. Lopez , D.V. Nanopoulos , R. Rangarajan and A. Zichichi , Light gravitino [34] M. Klasen and G. Pignol , New results for light gravitinos at hadron colliders: Tevatron limits [35] K. Mawatari and Y. Takaesu , HELAS and MadGraph with goldstinos , Eur. Phys. J. C 71 [36] P. de Aquino , F. Maltoni , K. Mawatari and B. Oexl , Light gravitino production in [37] M. Papucci , A. Vichi and K.M. Zurek , Monojet versus the rest of the world I: t-channel [38] A. Alloul , N.D. Christensen , C. Degrande , C. Duhr and B. Fuks , FeynRules 2. 0 - A complete toolbox for tree-level phenomenology , Comput. Phys. Commun . 185 ( 2014 ) 2250 [39] R. Casalbuoni , S. De Curtis , D. Dominici , F. Feruglio and R. Gatto , A gravitino-goldstino [40] R. Casalbuoni , S. De Curtis , D. Dominici , F. Feruglio and R. Gatto , High-energy equivalence [41] D.V. Volkov and V.A. Soroka , Higgs effect for Goldstone particles with spin 1/2 , JETP Lett. [42] S. Deser and B. Zumino , Broken supersymmetry and supergravity , Phys. Rev. Lett . 38 ( 1977 ) [44] H. Baer , K.-m. Cheung and J.F. Gunion , A heavy gluino as the lightest supersymmetric [47] N.D. Christensen et al., A comprehensive approach to new physics simulations, Eur. Phys. J. [48] C. Degrande et al., UFO - The Universal FeynRules Output, Comput. Phys. Commun . 183 [49] P. de Aquino, W. Link , F. Maltoni , O. Mattelaer and T. Stelzer , ALOHA: Automatic Commun . 183 ( 2012 ) 2254 [arXiv:1108. 2041 ] [INSPIRE]. [50] J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations , JHEP 07 ( 2014 ) [51] T. Sjostrand , S. Mrenna and P.Z. Skands , PYTHIA 6.4 physics and manual , JHEP 05 [52] DELPHES 3 collaboration , J. de Favereau et al., DELPHES 3, a modular framework for fast simulation of a generic collider experiment , JHEP 02 ( 2014 ) 057 [arXiv:1307.6346] [53] E. Conte , B. Fuks and G. Serret , MadAnalysis 5, a user-friendly framework for collider phenomenology , Comput. Phys. Commun . 184 ( 2013 ) 222 [arXiv:1206.1599] [INSPIRE]. [54] J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis , JHEP 07 ( 2002 ) 012 [hep-ph/0201195] [INSPIRE]. [55] W. Beenakker , R. Hopker , M. Spira and P.M. Zerwas , Squark and gluino production at hadron colliders, Nucl . Phys . B 492 ( 1997 ) 51 [hep-ph/9610490] [INSPIRE]. [56] D. Goncalves-Netto , D. Lopez-Val , K. Mawatari , T. Plehn and I. Wigmore , Automated squark and gluino production to next-to-leading order , Phys. Rev. D 87 (2013) 014002 [57] M. Cacciari , G.P. Salam and G. Soyez , The anti-kt jet clustering algorithm , JHEP 04 ( 2008 ) [58] J. Alwall , S. de Visscher and F. Maltoni , QCD radiation in the production of heavy colored particles at the LHC , JHEP 02 ( 2009 ) 017 [arXiv:0810.5350] [INSPIRE]. [59] C. Petersson , A. Romagnoni and R. Torre , Higgs decay with monophoton + MET signature from low scale supersymmetry breaking , JHEP 10 ( 2012 ) 016 [arXiv:1203.4563] [INSPIRE]. [60] M. Cacciari , G.P. Salam and G. Soyez , FastJet user manual , Eur. Phys. J. C 72 ( 2012 ) 1896


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP04%282015%29021.pdf

Fabio Maltoni, Antony Martini, Kentarou Mawatari, Bettina Oexl. Signals of a superlight gravitino at the LHC, Journal of High Energy Physics, 2015, 21, DOI: 10.1007/JHEP04(2015)021