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Register a new userA three-parameter neutrino mass matrix with maximal CP violation
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Using the seesaw mechanism, we construct a model for the light-neutrino Majorana mass matrix which yields trimaximal lepton mixing together with maximal CP violation and maximal atmospheric-neutrino mixing. We demonstrate that, in our model, the light-neutrino mass matrix retains its form under the one-loop renormalization-group evolution. With our neutrino mass matrix, the absolute neutrino mass scale is a function of |U_e3| and of the atmospheric mass-squared difference. We study the effective mass in neutrinoless double beta-decay as a function of |U_e3|, showing that it contains a fourfold ambiguity.
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The $mu$-$tau$ exchange symmetry in the neutrino mass matrix and its breaking as a perturbation are discussed. The exact $mu$-$tau$ symmetry restricts the 2-3 and 1-3 neutrino mixing angles as $theta_{23} = pi/4$ and $theta_{13} = 0$ at a zeroth order level. We claim that the $mu$-$tau$ symmetry breaking prefers a large CP violation to realize the observed value of $theta_{13}$ and to keep $theta_{23}$ nearly maximal, though an artificial choice of the $mu$-$tau$ breaking can tune $theta_{23}$, irrespective of the CP phase. We exhibit several relations among the deviation of $theta_{23}$ from $pi/4$, $theta_{13}$ and Dirac CP phase $delta$, which are useful to test the $mu$-$tau$ breaking models in the near future experiments. We also propose a concrete model to break the $mu$-$tau$ exchange symmetry spontaneously and its breaking is mediated by the gauge interactions radiatively in the framework of the extended gauge model with $B-L$ and $L_mu - L_tau$ symmetries. As a result of the gauge mediated $mu$-$tau$ breaking in the neutrino mass matrix, the artificial choice is unlikely, and a large Dirac CP phase is preferable.
In the flavor basis where the mass eigenstates of three charged leptons are identified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorana neutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3 neutrino mixing matrix V. In this treatment the unphysical phases of M_nu have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify M_nu to M_nu without any unphysical phases. We choose this special flavor basis and establish some exact analytical relations between the matrix elements of M_nu M_nu^dag and seven physical parameters --- three neutrino masses (m_1, m_2, m_3), three flavor mixing angles (theta_12, theta_13, theta_23) and the Dirac CP-violating phase (delta). Such results allow us to derive the conditions for the mu-tau flavor symmetry with theta_23 = pi/4 and maximal CP violation with delta = +/- pi/2, which should be useful for discussing specific neutrino mass models. In particular, we show that theta_23 = pi/4 and delta = +/- pi/2 keep unchanged when constant matter effects are taken into account for a long-baseline neutrino oscillation experiment.
In this paper, we consider the diagonal reflection symmetries and three-zero texture in the SM. The three-zero texture has two less assumptions ($(M_{u})_{11} , (M_{ u})_{11} eq 0$) than the universal four-zero texture for mass matrices $(M_{f})_{11} = (M_{f})_{13,31} = 0$ for $f = u,d, u, e$. The texture and symmetries reproduce the CKM and MNS matrices with accuracies of $O(10^{-4})$ and $O(10^{-3})$. By assuming a $d$-$e$ unified relation ($M_{d} sim M_{e}$), this system predicts the normal hierarchy, the Dirac phase $delta_{CP} simeq 202^{circ},$ the Majorana phases $alpha_{12} = 11.3^{circ}, alpha_{13} = 6.90^{circ}$ up to $pi$, and the lightest neutrino mass $m_{1} simeq 2.97,-,4.72,$[meV]. The effective mass of the double beta decay $|m_{ee}|$ is found to be $1.24 sim 1.77 ,$[meV].
Neutrino oscillation experiments under neutrino pair beam from circulating excited heavy ions are studied. It is found that detection of double weak events has a good sensitivity to measure CP violating parameter and distinguish mass hierarchy patterns in short baseline experiments in which the earth-induced matter effect is minimized.
It is shown that the bi-maximal solution is the only possibility to reconcile Zee-type neutrino mass matrix with three flavors to the current atmospheric and solar neutrino experimental data. The mass of the lightest neutrino, which consist mostly of $ u_{mu}$ and $ u_{tau}$, is $simeq Delta m_{odot}^2/(2sqrt{Delta m_{atm}^2})$. The related topics on Zee-type neutrino mass matrix are also discussed.
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