PHYSICAL REVIEW D 92, 115008 (2015) LHC constraints on gravitino dark matter † Alexandre Arbey Centre de Recherche Astrophysique de Lyon, Observatoire de Lyon, Saint-Genis Laval Cedex, F-69561, France; CNRS, UMR 5574, Ecole Normale Supérieure de Lyon, Université de Lyon, Université Lyon 1, F-69622 Villeurbanne Cedex, France; and CERN, CH-1211 Geneva, Switzerland Marco Battaglia* Santa Cruz Institute of Particle Physics, University of California at Santa Cruz, California 95064, USA and CERN, CH-1211 Geneva, Switzerland ‡ Laura Covi Institute for theoretical Physics, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany Jasper Hasenkamp§ Center for Cosmology and Particle Physics, New York University, New York, New York 10003, USA ∥ Farvah Mahmoudi Centre de Recherche Astrophysique de Lyon, Observatoire de Lyon, Saint-Genis Laval Cedex, F-69561 France; CNRS, UMR 5574, Université de Lyon, Université Lyon 1, F-69622 Villeurbanne Cedex, France; and CERN, CH-1211 Geneva, Switzerland (Received 11 September 2015; published 11 December 2015) Gravitino dark matter (DM) represents a compelling scenario in supersymmetry (SUSY), which brings together a variety of data from cosmology and collider physics. We discuss the constraints obtained from the LHC on supersymmetric models with gravitino dark matter and the neutralino next-to-lightest SUSY particle, which is the case most difficult to disentangle at colliders from a neutralino lightest SUSY particle forming DM. The phenomenological SUSY model with 19 þ 1 free parameters is adopted. Results are obtained from broad scans of the phase space of these uncorrelated parameters. The relation between gravitino mass, gluino mass and reheating temperature as well as the derived constraints on these parameters are discussed in detail. This relation offers a unique opportunity to place stringent bounds on the cosmological model, within the gravitino dark matter scenario, from the results of the LHC searches in run- 2 and the planned high-luminosity upgrade. DOI: 10.1103/PhysRevD.92.115008 PACS numbers: 11.30.Pb, 14.80.Ly, 14.80.Nb, 95.35.+d I. INTRODUCTION appears to be the most solid indication of new physics obtained so far, but the precision of the determination of its With the discovery of the Higgs boson at the LHC [1,2], relic density in the Universe, through the study of the collider particle physics moves on to a new phase, where cosmic microwave background (CMB) [3], and the increas- searches for new phenomena will be at the center of the ing sensitivity of the searches for DM scattering in under- physics program. Dark matter (DM) plays a special role in ground experiments [4–6] represent powerful constraints connecting these searches to cosmology. Not only DM for most models of new physics that offer a DM candidate. Supersymmetry (SUSY) is one of the most promising * and best motivated extensions of the Standard Model of Corresponding author. particle physics (SM), providing at the same time a solution [email protected] † alexandre.arbey@ens‑lyon.fr to the hierarchy problem within a weakly coupled theory, ‡ [email protected]‑goettingen.de radiative electroweak symmetry breaking with a light Higgs §[email protected] scalar with properties that, in the decoupling limit, come to ∥ [email protected] resemble those of the Standard Model, and also naturally includes several viable dark matter candidates within its Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- extensive particle spectrum. bution of this work must maintain attribution to the author(s) and Searches conducted at the LHC on the 7 þ 8 TeV run-1 the published article’s title, journal citation, and DOI. data have already set some significant constraints on low 1550-7998=2015=92(11)=115008(20) 115008-1 Published by the American Physical Society ALEXANDRE ARBEY et al. PHYSICAL REVIEW D 92, 115008 (2015) energy SUSY, in particular on the mass of the colored the LHC. After considering the present bounds on the superpartners and on the general mass scale in the case of model and how strongly the cosmological and astrophysi- highly constrained models, such as the constrained MSSM cal constraints limit the parameter space, we assess the (CMSSM) and the nonuniversal Higgs masses (NUHM) capability of the forthcoming LHC runs to test the gravitino models [7–9]. However, many scenarios with supersymmet- production mechanism and to tell the gravitino LSP from ric particles within the reach of the LHC runs at 13–14 TeVare the neutralino LSP solutions. totally unprobed at present, in particular when we consider Compared to previous studies, this analysis implements more general SUSY models [10–13] such as the “phenom- the latest collider constraints, including those from monojet enological MSSM” (pMSSM), without any assumption on searches which complement the other searches in the the SUSY breaking mediation mechanism and on unification regions of the parameter space with degenerate SUSY at high scale. This model gives the most general framework in masses, and we discuss the combination of LHC and other the minimal SUSYextension of the SM (MSSM) for studying data in the context of the gravitino models. We adopt the supersymmetric signals and constraints from colliders. It is pMSSM as a generic MSSM model that, contrary to more being adopted by an increasing number of phenomenological constrained models used in the past [33–39] for similar [14–27] and experimental [28,29] studies. studies, does not imply relations between the masses of the The particle most studied in conjunction with SUSY dark different SUSY particles. This opens up new regions of the 0 matter is the lightest neutralino, χ~1, which provides us with a parameter space with interesting phenomenology and viable realization of the WIMP mechanism and implies DM search opportunities at the LHC which were not available signals not only at colliders, but also in direct and indirect in the (CMSSM), as we demonstrate in this study. The detection. However, another very well-motivated SUSY concurrent analysis of the LHC data and the DM direct candidate for DM is the gravitino, G~ , the superpartner of detection experimental results will be key to identify a the graviton which couples with Planck-suppressed strength to neutralino NLSP signal without observation of the decay or the rest of the model, making it very difficult to detect in direct to exclude a large fraction of the model parameter space. or indirect DM experiments, in SUSY models with conserved The combination of the LHC sensitivity on the gluino mass R-parity. Even a small R-parity breaking opens up the and the requirement of a large enough reheating temper- – possibility of the gravitino decaying DM candidate relaxing ature after inflation for thermal leptogenesis [40 43] is part of the cosmological constraints [30]. Colliders offer a specific to the study performed in the pMSSM, restricts the uniqueway to probe the DM sector for scenarios with gravitino viable MSSM parameter space and highlights the capability dark matter. Therefore, dedicated searches should be actively of the LHC to test these cosmological scenarios. pursued to fully exploit the LHC reach in these scenarios. This paper is organized as follows: after discussing the In general, assuming that the gravitino is the lightest generalities of the gravitino LSP and DM scenario together SUSY particle (LSP) and forms DM greatly relaxes the DM with the cosmological bounds from nucleosynthesis in constraints on the SUSY spectrum, since its abundance is Sec. II, we describe our scan strategy for the pMSSM not produced through the WIMP mechanism and does not parameter space and the collider and low-energy con- only depend on the SUSY spectrum, but also on the straints in Sec. III. Section IV presents the results of our reheating temperature in the Universe after inflation analysis, while in Sec. V we give our conclusions. [31,32]. Consequently, the G~ remains a good candidate for DM even if the spectrum of the superpartners turns out II. GRAVITINO DARK MATTER to be much heavier than expected. Nevertheless, we will The gravitino is the superpartner of the graviton in show that the correlation between the gluino (and in general models with local supersymmetry [44]. It is the particle gaugino) mass and gravitino production ensures that the most directly related to the effect of SUSY breaking and LHC will be able to probe the gravitino production obtains its mass via the SuperHiggs mechanism [45] as mechanism for high reheating temperatures above the gauge-fermion of SUSY from any existing source of 9 10 GeV and that the high luminosity LHC program breaking. The hierarchy between the masses of the super- (HL-LHC) may play a crucial role for these tests. partners is determined by the particular mediation mecha- In this paper we present a study of the present and future nism, and it can result in a gravitino which is heavier, constraints on SUSY models with gravitino LSP respon- lighter or even much lighter than the other superpartners. If sible for DM and neutralino next-to-lightest SUSY particle the gravitino is the lightest SUSY state and therefore (NLSP). These models are not yet strongly constrained absolutely (or sufficiently) stable, it represents a viable since the current LHC limits on weakly produced SUSY candidate for explaining dark matter. The gravitino cou- particles are limited in coverage and our scenarios of plings are set by supergravity and by the MSSM parameters interest not easy to disentangle from those of neutralino and are inversely proportional to the reduced Planck mass, 18 LSP. Indeed, here we consider the parameter space where taken here at its standard value of MP ¼ 2.4 × 10 GeV. the neutralino is stable on collider time scales and gives rise The gravitino mass is the only additional parameter needed to the usual missing transverse energy (MET) signatures at to describe the gravitino and its interactions.