  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.
