Bi-Maximal Neutrino Mixing in SO(10)GUT

We find a grand unified SO(10) model which accommodates the bi-maximal neutrino mixing for vacuum-oscillation solutions to the atmospheric and the solar neutrino problems. This model maintains the original SO(10) mass relation between neutrino and up-type quark masses, mν2/mν3 ∼ (mc/mt). The recent data on the atmospheric neutrino from the SuperKamiokande (SuperK) Collaboration [1] have presented convincing evidence for neutrino oscillation with masssquared difference δmatm ≃ 5 × 10 eV. It is now understood that the long-standing puzzle of the atmospheric muon neutrino (νμ) deficit in underground detectors [2] is indeed due to the neutrino oscillation. As for the solar neutrino problem, there are still two allowed solutions : one is matter enhanced neutrino oscillation (i.e. the MSW solution [3]) and the other is long-distance vacuum neutrino oscillation called as “just-so” oscillation [5, 6]. It is known [7] that the small angle MSW solution and the maximal mixing between the atmospheric νμ and ντ are quite naturally explained in a large class of see-saw models [8]. However, the electron energy spectrum recently reported by the SuperK Collaboration [9] seems to favor the “just-so” vacuum oscillation with δmsun ≃ 10 eV and the maximal mixing. If this vacuum oscillation of the solar neutrino is confirmed in future solar-neutrino experiments [9, 10], we are led to a quite surprising situation that two independent mixing angles in the lepton sector are very large in contrast with the quark sector in which all observed mixing angles among different families are small. This may point to that a rule governs the lepton mass matrices is significantly different from the one for the quark sector, which seems to be a contradiction to the idea of complete unification of quarks and leptons. On the other hand, as noted recently by Barger et.al. [12] the required neutrino mass ratio mν2/mν3 ≃ 10 (provided mν1 ≪ mν2 ≪ mν3) is approximately equal to (mc/mt) as predicted by a see-saw model in the SO(10) grand unified theory (GUT) [13]. The purpose of this paper is to construct a simple SO(10)GUT model which naturally accomodates the bi-maximal neutrino mixing for the atmospheric and the solar neutrino vacuum oscillations, keeping the interesting SO(10)GUT mass relation mν2/mν3 ∼ (mc/mt) . We assume supersymmetry throughout this paper. Let us first discuss the minimal SO(10)GUT model which contains three families of 1 The MSW solution has two distinct regions : the small and the large angle ones [4]. 2 The so-called democratic mass matrices for quarks and leptons can generate large mixing in the neutrino sector [11]. 3 Recent analyses on phenomenological consequences of the bi-maximal neutrino mixing are given in Ref. [12, 14].