Charged lepton flavor violation in supersymmetry with bilinearR-parity violation

The simplest unified extension of the minimal supersymmetric standard model with bilinear R-parity violation naturally predicts a hierarchical neutrino mass spectrum, suitable to explain atmospheric and solar neutrino fluxes. We study whether the individual violation of the lepton numbers $L_{e,\mu ,\tau }$ in the charged sector can lead to measurable rates for $\mathrm{BR}\left(\overrightarrow{\mu }e\gamma \right)$ and $\mathrm{BR}\left(\overrightarrow{\tau }\mu \gamma \right).\mathrm{}$ We find that some of the R-parity violating terms that are compatible with the observed atmospheric neutrino oscillations could lead to rates for $\overrightarrow{\mu }e\gamma$ measurable in projected experiments. However, the $\Delta m_{12}^2$ obtained for those parameters is too high to be compatible with the solar neutrino data, excluding therefore the possibility of having measurable rates for $\overrightarrow{\mu }e\gamma$ in the model.