Searching for Gluino LSP at the LHC

We analyse relevant signals expected at the LHC, assuming that the gluino is the lightest supersymmetric particle (LSP) in the framework of the $\mu \nu$SSM. In this $R$-parity violating model, the presence of couplings involving right-handed neutrinos solves simultaneously the $\mu$ problem and the accommodations of neutrino masses and mixing angles. We study gluino pair production in quark-antiquark and gluon-gluon collisions. The main decay channels for the gluino LSP are the three-body decays to two quarks and a lepton or a neutrino. In both cases, the leading channels occur for the third family of quarks. We compare the predictions of this scenario with LHC searches for prompt and long-lived particles. To analyse the parameter space we sample the $\mu \nu$SSM for a gluino LSP, paying special attention to reproduce the current experimental data on neutrino and Higgs physics, as well as flavour observables. Our results imply a lower limit on the mass of the gluino LSP of about 2600 GeV, and an upper limit for the decay length of about 6 cm.