Prediction and its Stability in Neutrino Mass Matrix with Two Zeros

We have discussed predictions of Ue3 and JCP in the framework of the neutrino mass matrix with two zeros. The lower bound of Ue3 is 0.05, which depends on tan θ12 and tan θ23. We have investigated the stability of these predictions taking account of small corrections to zeros, which may come from radiative corrections or off-diagonal elements of the charged lepton mass matrix. We have found that the deviation from zeros is serious to predict |Ue3|. E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected] In these years empirical understanding of the mass and mixing of neutrinos have been advanced [1, 2, 3]. The KamLAND experiment selected the neutrino mixing solution that is responsible for the solar neutrino problem nearly uniquely [4], only large mixing angle solution. We have now good understanding concerning the neutrino mass difference squared (∆m atm , ∆m sun ) and neutrino flavor mixings (sin 2θatm, tan 2 θsun) [5]. A constraint has also been placed on the mixing from the reactor experiment of CHOOZ [6]. The texture zeros of the neutrino mass matrix have been discussed to explain these neutrino masses and mixings [7, 8, 9]. Recently, Frampton, Glashow and Marfatia [10] found acceptable textures of the neutrino mass matrix with two independent vanishing entries in the basis of the diagonal charged lepton mass matrix. The KamLAND result has stimulated the phenomenological analyses of the texture zeros [11, 12, 13, 14]. These results favour texture zeros for the neutrino mass matrix phenomenologically. However, there are theoretical problems. The first one is the effect of radiative corrections. A specific texture of the lepton mass matrix is not preserved to all orders. For example, nonzero components may evolve in zero-entries of the mass matrix at the low energy scale due to radiative corrections even if the zero texture is realized in the high energy scale. The second one is the choice of the flavor basis. In the model with some flavor symmetry, zeros of the neutrino mass matrix are given while the charged lepton mass matrix has off-diagonal components . Then, zeros of the neutrino mass matrix are polluted after diagonalizing the charged lepton mass matrix. Therefore we need to study the stability of predictions of the texture zeros by taking account of small corrections to zeros. In this paper, we present detail study of the neutrino mixing parameter Ue3 and CP violating quantity JCP [18], which are expected to be affected by the small corrections to zeros in the neutrino mass matrix. It is found that the predicted Ue3 and JCP considerably depend on these corrections. There are 15 textures with two zeros for the effective neutrino mass matrix Mν , which have five independent parameters. The two zero conditions give (Mν)ab = 3 ∑ i=1 UaiUbiλi = 0 , (Mν)αβ = 3 ∑ i=1 UαiUβiλi = 0 , (1) There are some models in which zeros of the neutrino mass matrix are realized in the diagonal basis of the charged lepton mass matrix [15, 16, 17]. 2 where λi is the i-th eigenvalue including the Majorana phase, and indices (ab) and (αβ) denote the flavor components, respectively. Solving these equations, the ratios of neutrino masses m1, m2, m3, which are absolute values of λi’s, are given in terms of the neutrino mixing matrix U [19] as follows: m1 m3 = ∣ ∣ ∣ ∣ ∣ Ua3Ub3Uα2Uβ2 − Ua2Ub2Uα3Uβ3 Ua2Ub2Uα1Uβ1 − Ua1Ub1Uα2Uβ2 ∣ ∣ ∣ ∣ ∣ , m2 m3 = ∣ ∣ ∣ ∣ ∣ Ua1Ub1Uα3Uβ3 − Ua3Ub3Uα1Uβ1 Ua2Ub2Uα1Uβ1 − Ua1Ub1Uα2Uβ2 ∣ ∣ ∣ ∣ ∣ . (2) Then, one can test textures in the ratio Rν , Rν ≡ ∣ ∣ ∣ ∣ ∣ m 2 −m2 1 m23 −m2 ∣ ∣ ∣ ∣ ∣ ≈ ∆m 2 sun ∆m2atm , (3) which has been given by the experimental data. The ratio Rν is given only in terms of four parameters (three mixing angles and one phase) in U = 