Lepton-flavor violation and $(g-2)_\mu$ in the $\mu\nu$SSM

Within framework of the $\mu$ from $\nu$ Supersymmetric Standard Model ($\mu\nu$SSM), exotic singlet right-handed neutrino superfields induce new sources for lepton-flavor violation. In this work, we investigate some lepton-flavor violating processes in detail in the $\mu\nu$SSM. The numerical results indicate that the branching ratios for lepton-flavor violating processes $\mu\rightarrow e\gamma$, $\tau\rightarrow\mu\gamma$ and $\mu\rightarrow3e$ can reach $10^{-12}$ when $\tan\beta$ is large enough, which can be detected in near future. We also discuss the constraint on the relevant parameter space of the model from the muon anomalous magnetic dipole moment. In addition, from the scalars for the $\mu\nu$SSM we strictly separate the Goldstone bosons, which disappear in the physical gauge.