Supersymmetry with spontaneous R-parity breaking in Z⁰ decays: The case of an additional Z

Single production of SUSY particles in the decays of the Z⁰ may proceed with large rates in models with spontaneously broken R-parity. We focus on the case where there is a lepton number symmetry as part of the gauge group. In the simplest of such models there is a single additional neutral gauge boson and the strength of R_p-violating interactions is related with that of the new gauge force. We study the phenomenological implications of the model for Z⁰ decays, including the study of the rates for single chargino production in Z⁰ decays, i.e. Z⁰→ξ^±τ^±, as well as for the so-called Zen events, and find that they may be measurable at LEP. The first process, characteristics of spontaneously broken R-parity models, may proceed with a branching ratio as large as few × 10^-5 and should lead to a very clear signature. Zen events have a different origin than in the minimal SUSY standard model (MSSM). Their rates may also be enhanced with respect to MSSM. Our estimates of these rates take into account all of the relevant observational constraints, such as those that follow from neutrinophyics, from precise Z⁰ property measurements, as well as SUSY particle searches at LEP.