Lepton flavor changing Higgs boson decays in SUSY with $\nu_R$

Lepton flavor violating Higgs boson decays (LFVHD) are studied in the context of the Minimal Supersymmetric Standard Model (MSSM) being embeded in a mSUGRA scenario that is enlarged with three right handed neutrinos and their supersymmetric partners, and with the neutrino masses being generated by the seesaw mechanism. We compute the partial widths for these decays to one-loop order and analyze numerically the corresponding branching ratios in terms of the mSUGRA and seesaw parameters. We analyze in parallel the lepton flavor changing $\l_j\to l_i \gamma$ decays and explore the maximum predicted rates for LFVHD, mainly for $H^0,A^0 \to \tau {\bar \mu}$ decays, by requiring compatibility with neutrino and $BR(\l_j\to l_i \gamma)$ data. We find LFVHD ratios of up to $10^{-5}$ in some regions of the MSSM-seesaw parameter space.