Anomalous magnetic moment of muon and L-violating Supersymmetric Models

We consider L-violating Supersymmetric Models to explain the recent muon $g_{\mu} -2$ deviation from the Standard Model. The order of trilinear L-violating couplings which we require also generate neutrino mass which is somewhat higher than expected unless one considers highly suppressed $L-R$ mixing of sfermions. However, without such fine tuning for sfermions it is possible to get appropriate muon $g_{\mu}-2$ deviation as well as neutrino mass if one considers some horizontal symmetry for the lepton doublet. Our studies show that $g_{\mu} -2$ deviation may not imply upper bound of about 500 GeV on masses of supersymmetric particles like chargino or neutralino as proposed by other authors for R parity conserving supersymmetric models. However, in our scenario sneutrino mass is expected to be light ($\sim 100$ GeV) and $e-\mu-\tau$ universality violation may be observed experimentally in near future.