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

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 (e(R),mu(R) or 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 approximate to 100% emitting a very soft (approximate to 1 MeV) photon which goes undetected. The spectroscopy of the 1S-state shows that it decays into two photons with Br approximate to 0.5 up to m(NLSP)approximate to 1 TeV. Thus NLSP sleptonium threshold production gives rise to the signal e(+)e(-)-> 2P -> 1S+"soft gamma"->gamma gamma which when compared with the standard model two-photon process (e(+)e(-)->gamma gamma ) has a statistical significance (SS=signal/noise) which, at an energy offset from threshold of E=20 GeV, goes from SS=11 to SS=2 when the mass of the NLSP ranges in the interval [100,200] GeV.