Neutrino mass matrix with U(2) flavor symmetry and neutrino oscillations

The three neutrino mass matrices in the SU(5) × U(2) model are studied focusing on the neutrino oscillation experiments. The atmospheric neutrino anomaly could be explained by the large νμ − ντ oscillation. The long baseline experiments are expected to detect signatures of the neutrino oscillation even if the atmospheric neutrino anomaly is not due to the neutrino oscillation. However, the model cannot solve the solar neutrino deficit while it could be reconciled with the LSND data. E-mail address: [email protected] The U(2) flavor symmetry [1, 2] is an interesting candidate for beyond SM. This flavor symmetry should be more precisely tested by future experiments [3]. The significant test will be possible in the neutrino sector as well as in the quark sector. The extension of the U(2) model to neutrino masses and mixings has been presented by Carone and Hall [4]. They have found that a simple modification is required for the flavor symmetry breaking pattern if the light three neutrino masses are obtained by the see-saw mechanism. This fact suggests that the U(2) symmetry will be tested seriously in neutrino oscillations. The purpose of our paper is to present the systematic analyses in order to clarify the phenomenological implications of the SU(5)×U(2) model in neutrino oscillations. In the U(2) flavor symmetry [1] the lighter two generations transform as a doublet and the third generation as a singlet of U(2). Only the third generation of the fermion can obtain a mass in the limit of unbroken symmetry limit. It is assumed that the quark and lepton mass matrices can be adequently described by VEV of flavons φ, S and A, in which S and A are symmetric and antisymmetric tensors, respectively. Furthermore, it is assumed 〈φ2〉/M = ǫ, 〈S22〉/M = ǫ and 〈A12〉/M = ǫ, where M is the cutoff scale of a flavon effective theory. Other VEV’s are assumed to be zero. Thus, the U(2) symmetry breaks to U(1) with breaking parameter ǫ and U(1) breaks to nothing with ǫ. The neutrino mass matrix has been discussed by Carone and Hall [4]. The righthanded Majorana mass matrix gives a zero Majorana mass due to the absence of the contribution from the antisymmetric flavon A. They proposed a simple solution which is to relax the assumptions: 〈φ1〉 = 0, 〈S11〉 = 0 and 〈S12〉 = 0. We present the systematic analyses of the modifed neutrino mass matrices focusing on neutrino oscillations. In the SU(5)×U(2) model, the modified Majorana mass matrix for the right-handed neutrinos is generated at leading order by the operators ΛR ( ν3ν3 + 1 M φνaν3 + 1 M φφνaνb + 1 M SΣY ΣY νaνb )