Atmospheric Neutrino Oscillation and Large Lepton-Flavour Violation in the SUSY SU(5) GUT

The atmospheric neutrino anomaly reported by the super-Kamiokande collaboration suggests existence of a large flavour violating Yukawa coupling in the lepton sector. We discuss lepton-flavour violation at low energies in the framework of the supersymmetric SU(5)GUT model with right-handed neutrinos. We find that for a wide range of parameter space suggested from the atmospheric neutrino anomaly, if the tau-neutrino Yukawa coupling is as large as that of top quark, lower bounds of the branching ratios of μ+ → e+γ, τ → μγ, and the μ− e conversion rate on 48 22Ti become around 10−14, 10−9, and 10−16, respectively. These reaction rates may be in the region accessible by near future experiments. Small dimensional parameters in physics were often important indications of new, more fundamental physics in the past. A neutrino mass is considered as such an example in the present particle physics. The see-saw mechanism [1] is the most attractive theory for light massive neutrinos in which the smallness of their masses is naturally explained by large Majorana masses of their chiral partners (i.e. righthanded neutrinos). At present there are two experimental hints of nonvanishing neutrino masses: one is the well-known solar neutrino deficit [2] and the other is the atmospheric neutrino anomaly [3]. A recent report on the atmospheric neutrino from the superKamiokande collaboration [4] has presented convincing evidence that the atmospheric neutrino anomaly is indeed due to neutrino oscillation. From the zenith-angle dependence of the ratio of νe and νμ fluxes the super-Kamiokande collaboration [4] has suggested a neutrino mass difference as δm2νμνX ≃ (10 −3 − 10)eV. (1) Provided mass hierarchymντ > mνμ > mνe it is natural to consider νX = ντ while the solar neutrino deficit is explained by the matter oscillation between νμ and νe [5]. Thus, the atmospheric neutrino anomaly implies a nonvanishing neutrino mass, mντ ≃ (0.03− 0.1)eV, (2) which suggests the presence of right-handed neutrinos at the scale ∼ (10 − 10) GeV. This may support strongly supersymmetric (SUSY) grand unified theories (GUT’s), since the mass of the right-handed neutrino is very close to the GUT scale ≃ 10GeV. The other important feature of the super-Kamiokande observation is that a large mixing sin 2θνμντ ≃ 1 (3) is required to account for the atmospheric neutrino anomaly. This result already indicates a large lepton-flavour violation (LFV) at the GUT scale. In this letter we point out that Yukawa interactions for the right-handed neutrinos in the