The minimal theory for R-parity violation at the LHC

We investigate the simplest gauge theory for spontaneous R-parity breaking and its testability at the LHC. This theory, based on a local B-L gauge symmetry, can be considered as the simplest framework for understanding the origin of the R-parity violating interactions, giving rise to potential lepton number violating signals and suppressed baryon number violating operators. The full spectrum of the theory and the constraints coming from neutrino masses are analyzed in detail. We discuss the proton decay issue and the possible dark matter candidates. In order to assess the testability of the theory we study the properties of the new gauge boson, the neutralino decays and the main production channels for the charged sleptons at the LHC. We find that final states with four charged leptons, three of them with the same-sign, and four jets are the most striking signals for the testability of the lepton number violation associated with spontaneous R-parity violation at the LHC.