Search for long-lived stopped gluino $R$-hadrons decaying out-of-time with LHC collisions in 2011 and 2012 using the ATLAS detector

$R$-hadrons are composite, massive, long-lived particles predicted in several scenarios of physics beyond the Standard Model, such as split supersymmetry. An updated search is performed for gluino $R$-hadrons which have come to rest within the ATLAS calorimeter, and decay at some later time to a gluon or $q\bar{q}$ pair and a neutralino. Candidate decay events are triggered in the empty bunch crossings of the LHC in order to remove $pp$ collision backgrounds. Selections based on jet shape and muon-system activity are applied to discriminate events from cosmic ray and beam-halo muon backgrounds. In the absence of an excess, improved limits are set on the gluino mass, for different gluino decays, gluino lifetimes, and neutralino masses. With a neutralino of mass 100 GeV, the analysis excludes $m_{\tilde{g}} < 857$ GeV ($763$ GeV expected), for a gluino lifetime between 10 $\mu s$ and 1000 $s$ in the generic $R$-hadron model with equal decays to $q\bar{q}\tilde{\chi}^0$ and $g\tilde{\chi}^0$.