Analysis of the parameter space and spectrum of the $\mu \nu$SSM
  The $\mu\nu$SSM is a supersymmetric standard model that solves the $\mu$ problem of the MSSM using the R-parity breaking couplings between the right-handed neutrino superfields and the Higgses in the superpotential, $\lambda_{i} \hat \nu^c_i \hat H_d \hat H_u$. The $\mu$ term is generated spontaneously through sneutrino vacuum expectation values, $\mu=\lambda_i < \tilde \nu^c_i>$, once the electroweak symmetry is broken. In addition, the couplings $\kappa_{ijk} \hat \nu^c_i\hat \nu^c_j\hat \nu^c_k$ forbid a global U(1) symmetry avoiding the existence of a Goldstone boson, and also contribute to spontaneously generate Majorana masses for neutrinos at the electroweak scale. Following this proposal, we have analysed in detail the parameter space of the $\mu\nu$SSM. In particular, we have studied viable regions avoiding false minima and tachyons, as well as fulfilling the Landau pole constraint. We have also computed the associated spectrum, paying special attention to the mass of the lightest Higgs. The presence of right and left-handed sneutrino vacuum expectation values leads to a peculiar structure for the mass matrices. The most important consequence is that neutralinos are mixed with neutrinos, and neutral Higgses with sneutrinos. 
Nicolas Escudero, Daniel E. Lopez-Fogliani, Carlos Munoz, Roberto Ruiz   de Austri