Study of the Gauge Mediation Signal with Non-pointing Photons at the CERN LHC

In this paper we study the gauge mediation signal with the ATLAS detector at the CERN LHC. We focus on the case where the NLSP is the long-lived lightest neutralino ($\tilde{\chi}^0_1$) which decays dominantly into a photon ($\gamma$) and a gravitino ($\tilde{G}$). A non-pointing photon from the neutralino decay can be detected with good position and time resolutions by the electormagnetic calorimeter (ECAL), while the photon momentum would be precisely measured if the photon is 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 non-pointing photon arising from the cascade decay $\tilde{\ell}\to \ell\tilde{\chi}^0_1\to \ell\gamma \tilde{G}$. A Monte Carlo simulation at a sample point shows that the masses would be measured with an error of 3% for $\cal{O}$(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 $\cal{O}$(10) m.