Supersymmetry and large transition magnetic moment of the neutrino

We show that the most general minimal supersymmetric standard model with ${\mathit{l}}_{\mathit{e}}$-${\mathit{l}}_{\mathrm{\mu }}$ symmetry (${\mathit{l}}_{\mathit{i}}$=ith lepton number) and a discrete horizontal symmetry between e and μ families can generate a large transition magnetic moment for the neutrino while leading to a naturally small mass. A magnetic moment of order ${\mathrm{\mu }}_{\nu }$≊0.3×${10}^{\mathrm{-}10}$ ${\mathrm{\mu }}_{\mathit{B}}$ implies ${\mathit{m}}_{\nu \mathit{e}}$=${\mathit{m}}_{\nu \mathrm{\mu }}$≥1 eV. The photino, which is expected to be the lightest supersymmetric particle, is unstable in this scheme, decaying dominantly into three-lepton final states (${\mathrm{\mu }}^{+}$ν${\mathrm{¯}}_{\mathit{e}}$ ${\mathrm{\tau }}^{\mathrm{-}}$, ${\mathrm{e}}^{+}$ν${\mathrm{¯}}_{\mathrm{\mu }}$ ${\mathrm{\tau }}^{\mathrm{-}}$+charge conjugate).