Neutrino masses, muon g−2, and lepton-flavour violation in the supersymmetric see-saw model

In the light of the recent muon (gμ−2) result by the E821 experiment at the Brookhaven National Laboratory, we study the event rates of the charged lepton-flavour-violating (LFV) processes in the supersymmetric standard model (SUSY SM) with the heavy right-handed neutrinos (SUSY see-saw model). Since the left-handed sleptons get the LFV masses via the neutrino Yukawa interaction in this model, the event rate of μ→eγ and the SUSY-SM correction to (gμ−2)/2 (δaμSUSY) are strongly correlated. When the left-handed sleptons have a LFV mass between the first and second generations ((m2L̃)12) in the mass matrix, it should be suppressed by ∼10−3 (10−9/δaμSUSY) compared with the diagonal components (mSUSY2), from the current experimental bound on μ→eγ. The recent (gμ−2) result indicates δaμSUSY∼10−9. The future charged LFV experiments could cover (m2L̃)12/mSUSY2≳10−(5–6). These experiments will give a significant impact on the flavour models and the SUSY-breaking models. In the SUSY see-saw model (m2L̃)12 is proportional to square of the tau-neutrino Yukawa-coupling constant. In the typical models where the neutrino-oscillation results are explained and the top-quark and tau-neutrino Yukawa couplings are unified at the GUT scale, a large LFV mass of (m2L̃)12/mSUSY2≳10−4 is generated, and the large LFV event rates are predicted. We impose a so-called no-scale condition for the SUSY-breaking parameters at the GUT scale, which suppresses the FCNC processes, and derive the conservative lower bound on μ→eγ. The predicted Br(μ→eγ) could be covered at the future LFV experiments.