Deviation of Neutrino Mixing from Bi-maximal

We have studied how observables of the neutrino mixing matrix can link up with the ones in the quark sector. The deviation from the bi-maximal flavor mixing is parameterized using a 3 × 3 unitary matrix. The neutrino mixings are investigated supposing this unitary matrix to be hierarchical like the quark mixing matrix. We obtain the remarkable prediction |Ue3| ≥ 0.03 from the experimentally allowed range tan θsol = 0.24 ∼ 0.89. The CP violation in neutrino oscillations is expected to be very small. E-mail address: [email protected] E-mail address: [email protected] Recent data from the Super-Kamiokande [1, 2] and SNO (Sudbury Neutrino Observatory) [3] experiments have provided model independent evidences in favor of oscillations of atmospheric and solar neutrinos. The disappearance of atmospheric νμ’s measured in the Super-Kamiokande experiment [1] has been confirmed by the MACRO [4] and Soudan 2 [5] experiments, and by the K2K long-baseline experiment [6]. The Super-Kamiokande [7] and MACRO [4] atmospheric neutrino data favor the νμ → ντ process. The solar neutrino data of the Super-Kamiokande [2] and SNO [3] experiments show in a model independent way that νe → νμ,τ transitions take place. This evidence agrees with the comparison of the Solar Standard Model [8] predictions with the data of the other solar neutrino experiments (Homestake, GALLEX, SAGE, GNO [9]). The global analysis of all solar neutrino data in terms of νe → νμ,τ oscillations [10, 11] favor strongly the Large Mixing Angle (LMA) MSW solution [12]. These experimental results indicate that neutrinos are massive and mixed particles [13, 14] and the flavor mixing of neutrinos is bi-large, i.e. close to bi-maximal [15]. This means that the neutrino flavor mixing is very different from the one in the quark sector. It is therefore important to investigate how the observables of the neutrino mixing matrix [16] can link up with those in the quark sector [17]. In the recent experimental data, the neutrino flavor mixings deviate from the bimaximal flavor mixing as follows [11, 18]: sin 2θatm > 0.83 (99 % C.L.) , tan θsol = 0.24 ∼ 0.89 (99.73 % C.L.) . (1) One may consider seriously the deviation [19] from the bi-maximal flavor mixing [15]. In this paper, we discuss the deviation from the bi-maximal flavor mixing of neutrinos by linking it up phenomenologically with the quark flavor mixing. In our naive understanding it is natural that the charged lepton mass matrix has a structure similar