Sleptonium at the linear collider and the slepton co-next-to-lightest supersymmetric particle scenario in gauge mediated symmetry breaking models

Abstract

We discuss the possibility of formation and subsequent detection of a supersymmetric bound state composed of a slepton-antislepton pair at the next linear collider. The Green function method is used within a nonrelativistic approximation to estimate the threshold production cross section of the $2P$ bound state. The parameter space of gauge mediated symmetry breaking (GMSB) models allow a particular scenario in which a charged slepton (${\stackrel{\texttildelow{}}{e}}_{R},{\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$ or ${\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}$) is the next-to-lightest supersymmetric particle (NLSP). Within this scenario the produced $2P$ bound-state decays, through a dipole transition, into the $1S$ ground-state with branching ratio $\ensuremath{\approx}100%$ emitting a very soft ($\ensuremath{\approx}1\text{ }\text{ }\mathrm{MeV}$) photon which goes undetected. The spectroscopy of the $1S$-state shows that it decays into two photons with $\mathrm{Br}\ensuremath{\approx}0.5$ up to ${m}_{\mathrm{NLSP}}\ensuremath{\approx}1\text{ }\text{ }\mathrm{TeV}$. Thus NLSP sleptonium threshold production gives rise to the signal ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}2P\ensuremath{\rightarrow}1S+``\mathrm{soft}\text{ }\text{ }\ensuremath{\gamma}''\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ which when compared with the standard model two-photon process (${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ ) has a statistical significance ($SS=$signal/noise) which, at an energy offset from threshold of $E=20\text{ }\text{ }\mathrm{GeV}$, goes from $SS=11$ to $SS=2$ when the mass of the NLSP ranges in the interval $[100,200]\text{ }\text{ }\mathrm{GeV}$.