Measuring gauge-mediated supersymmetry breaking parameters at a 500 GeV $e^+e^-$ linear collider

Abstract.

We consider the phenomenology of a class of gauge-mediated supersymmetry (SUSY) breaking (GMSB) models at a $e^+e^-$ Linear Collider (LC) with $E_{\rm c.o.m.}$ up to 500 GeV. In particular, we refer to a high-luminosity (${\cal L} \sim 3 \times 10^{34}$ cm$^{-2}$ s$^{-1}$) machine, and use detailed simulation tools for a proposed detector. Among the GMSB-model building options, we define a simple framework and outline its predictions at the LC, under the assumption that no SUSY signal is detected at LEP or Tevatron. We assess the potential of the LC to distinguish between the various SUSY model options and to measure the underlying parameters with high precision, including for those scenarios where a clear SUSY signal would have already been detected at the LHC before starting the LC operations. Our focus is on the case where a neutralino ($\tilde N_1$) is the next-to-lightest SUSY particle (NLSP), for which we determine the relevant regions of the GMSB parameter space. Many observables are calculated and discussed, including production cross sections, NLSP decay widths, branching ratios and distributions, for dominant and rare channels. We sketch how to extract the messenger and electroweak scale model parameters from a spectrum measured via, e.g. threshold-scanning techniques. Several experimental methods to measure the NLSP mass and lifetime are proposed and simulated in detail. We show that these methods can cover most of the lifetime range allowed by perturbativity requirements and suggested by cosmology in GMSB models. Also, they are relevant for any general low-energy SUSY breaking scenario. Values of $c\tau_{\tilde N_1}$ as short as 10's of $\mu$m and as long as 10's of m can be measured with errors at the level of 10% or better after one year of LC running with high luminosity. We discuss how to determine a narrow range ($\lesssim 5\%$) for the fundamental SUSY breaking scale $\sqrt{F}$, based on the measured $m_{\tilde N_1}$, $c\tau_{\tilde N_1}$. Finally, we suggest how to optimise the LC detector performance for this purpose.