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We analyze the anomalous magnetic moment of the muon $g-2$ in the$\mu\nu$SSM. This $R$-parity violating model solves the $\mu$ problemreproducing simultaneously neutrino data, only with the addition ofright-handed neutrinos. In the framework of the $\mu\nu$SSM, light leftmuon-sneutrino and wino masses can be naturally obtained driven by neutrinophysics. This produces an increase of the dominant chargino-sneutrino loopcontribution to muon $g-2$, solving the gap between the theoretical computationand the experimental data. To analyze the parameter space, we sample the$\mu\nu$SSM using a likelihood data-driven method, paying special attention toreproduce the current experimental data on neutrino and Higgs physics, as wellas flavor observables such as $B$ and $\mu$ decays. We then apply theconstraints from LHC searches for events with multi-leptons + MET on the viableregions found. They can probe these regions through chargino-chargino,chargino-neutralino and neutralino-neutralino pair production. We conclude thatsignificant regions of the parameter space of the $\mu\nu$SSM can explain muon$g-2$ data.

Explaining muon $g-2$ data in the $\mu\nu$SSM