Study of the gauge mediation signal at the CERN LHC

In this note we study the gauge mediation signal with the ATLAS detector at the CERN Large Hadron Collider. We focus on the case where the next lightest supersymmetric particle is the long-lived lightest neutralino ($\tilde{\chi}^0_1$), which decays predominantly into a photon ($\gamma$) and a gravitino ($\tilde{G}$). A nonpointing photon from the neutralino decay can be detected with good position and time resolution by the electromagnetic calorimeter (ECAL), while the photon momentum could be precisely measured if the photon were converted inside the inner tracking detector before reaching the ECAL. A new technique is developed to determine the masses of the slepton ($\tilde{\ell}$) and the neutralino from events with a lepton and a converted nonpointing photon arising from the cascade decay $\tilde{\ell}\rightarrow \ell\tilde{\chi}^0_1\rightarrow \ell\gamma \tilde{G}$. A Monte Carlo simulation at a sample point shows that the masses would be measured with an error of 3\% for ${O}$(100) selected $\ell\gamma$ pairs. Once the sparticle masses are determined by this method, the decay time and momentum of the neutralino are solved using the ECAL data and the lepton momentum only, for all $\ell\gamma$ pairs without the photon conversion. We estimate the sensitivity to the neutralino lifetime for $c\tau=10$~cm to ${O}$(10)~m.