Precise prediction for the Higgs-boson masses in the

The $$\mu \nu \mathrm {SSM}$$ 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 $$\mu \nu \mathrm {SSM}$$ with one generation of right-handed neutrinos in a mixed on-shell/$${\overline{\mathrm {DR}}}$$ 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 non-flavor-diagonal soft mass parameters, which have their origin in the breaking of R-parity in the $$\mu \nu \mathrm {SSM}$$. We calculate the full one-loop corrections to the neutral scalar masses of the $$\mu \nu \mathrm {SSM}$$. 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 $$\mu \nu \mathrm {SSM}$$-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 $$\mu \nu \mathrm {SSM}$$ are at the same level of accuracy as in the NMSSM. Finally we show that the $$\mu \nu \mathrm {SSM}$$ can accomodate a Higgs boson that could explain an excess of $$\gamma \gamma $$ events at $$\sim 96 \,\mathrm {GeV}$$ as reported by CMS, as well as the $$2\,\sigma $$ excess of $$b \bar{b}$$ events observed at LEP at a similar mass scale