Spontaneous R-parity violation: Lightest neutralino decays and neutrino mixing angles at future colliders

We study the decays of the lightest supersymmetric particle (LSP) in models with spontaneously broken R-parity. We focus on the two cases that the LSP is either a bino or a neutral singlet lepton. We work out the most important phenomenological differences between these two scenarios and discuss also how they might be distinguished from explicit R-parity breaking models. In both cases we find that certain ratios of decay branching ratios are correlated with either the solar or the atmospheric (and reactor) neutrino angle. The hypothesis that spontaneous R-parity violation is the source of the observed neutrino masses is therefore potentially testable at the LHC.