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

We study a distinct supersymmetric signal of multi- photonsin association with jets and missing transverse energy. At least one of these photonshas the origin in displaced vertex, thus delayed and non-pointing. We consider a supersymmetric scenario in which the gravitinois the lightest supersymmetric particle(LSP) (with a mass $\sim 1~{keV}$) and the lightest neutralinois the next-to- lightest supersymmetric particle(NLSP). The NLSP decays dominantly into a photonand a gravitinowithin the detector with a decay length ranging from $c\tau_{\ tilde{\chi}}\sim$ 50-100 cm. In addition, we assume that the second lightest neutralinoand the lightest neutralinoare nearly degenerate and this leads to a prompt radiative decay of the next-to-lightest neutralinointo a photonand a lightest neutralinowith a large branching ratio. Such degenerate neutralinoscan be realised in various representations of the $SU(5)$, $ SO(10)$, and $E(6)$ Grand Unified Theories(GUTs). The non-pointing photonscan 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- photonevents and a few four- photonsevents at the LHC, in addition to several thousands di- photonevents. We also predict the event rates even at the early phase of LHC run.