Impact of Higgs physics on the parameter space of the $\mu\nu$SSM

Given the increasing number of experimental data, together with the precise measurement of the properties of the Higgs boson at the LHC, the parameter space of supersymmetric models starts to be constrained. We carry out a detailed analysis of this issue in the framework of the $\mu\nu$SSM. In this model, three families of right-handed neutrino superfields are present in order to solve the $\mu$ problem and simultaneously reproduce neutrino physics. The new couplings and sneutrino vacuum expectation values in the $\mu\nu$SSM induce new mixing of states, and, in particular, the three right sneutrinos can be substantially mixed with the neutral Higgses. After diagonalization, the masses of the corresponding three singlet-like eigenstates can be smaller or larger than the mass of the Higgs, or even degenerated with it. We analyze whether these situations are still compatible with the experimental results. To address it we scan the parameter space of the Higgs sector of the model. In particular, we sample the $\mu\nu$SSM using a powerful likelihood data-driven method, paying special attention to satisfy the constraints coming from Higgs sector measurements/limits (using HiggsBounds and HiggsSignals), as well as a class of flavor observables such as $B$ and $\mu$ decays, while muon $g-2$ is briefly discussed. We find that large regions of the parameter space of the $\mu\nu$SSM are viable, containing an interesting phenomenology that could be probed at the LHC.