Multi-photon signal in supersymmetry comprising non-pointing photon(s) at the LHC

We study a distinct supersymmetric signal of multi-photons in association with jets and missing transverse energy. At least one of these photons has the origin in displaced vertex, thus delayed and non-pointing. We consider a supersymmetric scenario in which the gravitino is the lightest supersymmetric particle (LSP) (with a mass $\sim 1~{keV}$) and the lightest neutralino is the next-to-lightest supersymmetric particle (NLSP). The NLSP decays dominantly into a photon and a gravitino within the detector with a decay length ranging from $c\tau_{\tilde{\chi}}\sim$ 50-100 cm. In addition, we assume that the second lightest neutralino and the lightest neutralino are nearly degenerate and this leads to a prompt radiative decay of the next-to-lightest neutralino into a photon and a lightest neutralino with a large branching ratio. Such degenerate neutralinos can be realised in various representations of the $SU(5)$, $SO(10)$, and $E(6)$ Grand Unified Theories (GUTs). The non-pointing photons can be reconstructed at the electromagnetic calorimeter of the ATLAS inner-detector, which have been designed with good timing and directional resolution. We find that with a centre-of-mass energy $E_{cm}=14 ~{TeV}$ at an integrated luminosity of 100 $fb^{-1}$ one may see evidence of hundreds of tri-photon events and a few four-photons events at the LHC, in addition to several thousands di-photon events. We also predict the event rates even at the early phase of LHC run.