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 leptonflavour-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 (δaSUSY μ ) are strongly correlated. When the left-handed sleptons have a LFV mass between the first and second generations ((m2 L̃ )12) in the mass matrix, it should be suppressed by ∼ 10−3 (10−9/δaSUSY μ ) compared with the diagonal components (mSUSY), from the current experimental bound on μ → eγ. The recent (gμ − 2) result indicates δaSUSY μ ∼ 10−9. The future charged LFV experiments could cover (m2 L̃ )12/m 2 SUSY ∼ 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 (m2 L̃ )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 (m2 L̃ )12/m 2 SUSY ∼ 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. Various neutrino oscillation experiments suggest the existence of lepton-flavour violation (LFV). The atmospheric neutrino result by the superKamiokande experiment is a convincing evidence of the neutrino mixing between νμ and ντ [1]. Solar neutrino experiments have also strongly indicated the mixing between νe and νμ or ντ [2]. These results are explained by the tiny but non-zero neutrino masses, and the natural model for the neutrino masses is the see-saw mechanism [3]. It has been discussed that the supersymmetric (SUSY) extension of the see-saw mechanism (SUSY see-saw model) could lead to the charged-LFV processes, such as μ → eγ [4, 5, 6, 7, 8]. If the SUSY-breaking terms in the supersymmetric standard model (SUSY SM) are generated by the interaction at the gravitational scale or the GUT scale, the Yukawa interaction of the right-handed neutrinos generates the LFV masses for the lefthanded sleptons radiatively, and the LFV masses are a direct source of the charged-LFV processes in the SUSY SM. Especially, in the SUSY models with Yukawa-coupling unification between the top quark and tau neutrino, the event rates of the charged-LFV processes are significantly enhanced, since the LFV masses is proportional to square of the tau-neutrino Yukawa-coupling constant. In many proposed models, this assumption is adopted so that the fermion mass structure, including the neutrino sector, is explained in a unified picture between quarks and leptons, of which a well-known example is the SO(10) GUT. If the left-handed slepton, chargino and neutralino are light, the predicted event rates could be within reach of the near-future experiments. Recently, the ongoing E821 experiment at the Brookhaven National Laboratory updated the result for the muon anomalous magnetic moment (gμ − 2) [9], and it is found that (gμ − 2) is about 2.6σ away from the SM prediction as aμ(exp)− aμ(SM) = 43(16)× 10−10. (1) This suggests that new physics exists around the TeV scale [10], and this result will be further refined after including the data for the 2000 run. The SUSY SM predicts a sizable deviation from the SM prediction for (gμ − 2) [11], and it is a good candidate to accommodate the (gμ − 2) result [12]. This comes from the fact that the dominant correction to (gμ − 2) in the SUSY SM is from a one-loop diagram of chargino and muon sneutrino and it is proportional to tanβ. This new observation indicates that the chargino,