Charged lepton Flavor Violation in Supersymmetry with Bilinear R-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 ${L}_{e,\ensuremath{\mu},\ensuremath{\tau}}$ in the charged sector can lead to measurable rates for $\mathrm{BR}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma})$ and $\mathrm{BR}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}).$ We find that some of the R-parity violating terms that are compatible with the observed atmospheric neutrino oscillations could lead to rates for $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ measurable in projected experiments. However, the $\ensuremath{\Delta}{m}_{12}^{2}$ obtained for those parameters is too high to be compatible with the solar neutrino data, excluding therefore the possibility of having measurable rates for $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ in the model.