  The supersymmetric standard model with right-handed neutrino supermultiplets
generically contains a soft supersymmetry breaking mass term: $\delta L ={1
\over 2} B_\nu M\tilde{\nu}_R \tilde {\nu}_R$. We call this operator the
"neutrino $B$-term". We show that the neutrino $B$-term can give the dominant
effects from the neutrino sector to lepton flavor violating processes and to
lepton electric dipole moments.
