LHC phenomenology of the mu nu SSM

The $\mu\nu$SSM has been proposed to solve simultaneously the $\mu$-problem of the MSSM and explain current neutrino data. The model breaks lepton number as well as R-parity. In this paper we study the phenomenology of this proposal concentrating on neutrino masses and the decay of the lightest supersymmetric particle (LSP). At first we investigate in detail the $\mu\nu$SSM with one generation of singlets, which can explain all neutrino data, once 1-loop corrections are taken into account. Then we study variations of the model with more singlets, which can generate all neutrino masses and mixings at tree-level. We calculate the decay properties of the lightest supersymmetric particle, assum…