Analysis of the long-lived slepton next-to-lightest supersymmetric particle in the gauge-mediated supersymmetry breaking model at a linear collider

We performed an analysis on the detection of a long-lived slepton at a linear collider with $\sqrt{s}=500\mathrm{}\hspace{0.5em}\mathrm{GeV}.$ In gauge-mediated symmetry breaking models a long-lived NLSP is predicted for a large value of the supersymmetry breaking scale $\sqrt{F}.$ Furthermore in a large portion of the parameter space this particle is a stau. Such heavy charged particles will leave a track in the tracking volume and hit the muonic detector. In order to disentangle this signal from the muon background, we explore the kinematics and particle identification tools: a time-of-flight device, $dE/dX,$ and Cherenkov devices. We show that a linear collider will be able to detect long-lived staus with masses up to the kinematical limit of the machine. We also present our estimation of the sensitivity to the stau lifetime.