Precise prediction for the Higgs-boson masses in the μνSSM

The mu nu SSM is a simple supersymmetric extension of the Standard Model (SM) capable of predicting neutrino physics in agreement with experiment. In this paper we perform the complete one-loop renormalization of the neutral scalar sector of the it mu nu SSM with one generation of right-handed neutrinos in a mixed on-shell/(DR) over bar scheme. The renormalization procedure is discussed in detail, emphasizing conceptual differences to the minimal (MSSM) and next-to-minimal (NMSSM) supersymmetric standard model regarding the field renormalization and the treatment of nonflavor-diagonal soft mass parameters, which have their origin in the breaking of R-parity in the mu nu SSM. We calculate the full one-loop corrections to the neutral scalar masses of the mu nu SSM. The one-loop contributions are supplemented by available MSSM higher-order corrections. We obtain numerical results for a SM-like Higgs boson mass consistent with experimental bounds. We compare our results to predictions in the NMSSM to obtain a measure for the significance of genuine it mu nu SSM-like contributions. We only find minor corrections due to the smallness of the neutrino Yukawa couplings, indicating that the Higgs boson mass calculations in the mu nu SSM are at the same level of accuracy as in the NMSSM. Finally we show that the mu nu SSM can accomodate a Higgs boson that could explain an excess of gamma gamma events at similar to 96 GeV as reported by CMS, as well as the 2 sigma excess of b (b) over bar events observed at LEP at a similar mass scale.