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Current experimental data on neutrino mixing are very well described by TriBiMaximal mixing. Accordingly, any phenomenological parametrization of the MNSP matrix must build upon TriBiMaximal mixing. We propose one particularly natural parametrization, which we call TriMinimal. The three small deviations of the PDG angles from their TriBiMaximal values, and the PDG phase, parametrize the TriMinimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical neutrinos. As no foreseeable experiment will be sensitive to more than second order in the small parameters, we expand these flavor probabilities to second order.
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Starting from a new zeroth order basis for quark mixing (CKM) matrix based on the quark-lepton complementarity and the tri-bimaximal pattern of lepton mixing, we derive a triminimal parametrization of CKM matrix with three small angles and a CP-violating phase as its parameters. This new triminimal parametrization has the merits of fast convergence and simplicity in application. With the quark-lepton complementary relations, we derive relations between the two unified triminimal parametrizations for quark mixing obtained in this work and for lepton mixing obtained by Pakvasa-Rodejohann-Weiler. Parametrization deviating from quark-lepton complementarity is also discussed.
A new and novel idea for a predictive neutrino mass matrix is presented, using the non-Abelian discrete symmetry A(4) and the seesaw mechanism with only two heavy neutral fermion singlets. Given the components of the one necessarily massless neutrino eigenstate, the other two massive states are automatically generated. A realistic example is discussed with predictions of a normal hierarchy of neutrino masses and maximal CP violation.
We show that the Kobayashi-Maskawa (KM) parametrization of the 3 X 3 lepton flavor mixing matrix is a useful language to describe the phenomenology of neutrino oscillations. In particular, it provides us with a convenient way to link the genuine flavor mixing parameters (theta_1, theta_2, theta_3 and delta_KM) to their effective counterparts in matter (tilde{theta}_1, tilde{theta}_2, tilde{theta}_3 and tilde{delta}_KM). We rediscover the Toshev-like relation sin tilde{delta}_KM sin 2tilde{theta}_2 = sin delta_KM sin 2theta_2 in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matter-corrected flavor mixing parameters in two different experimental scenarios: (a) the neutrino beam energy E is above O(1) GeV and (b) E is below O(1) GeV. As an example, the probability of u_mu -> u_e oscillations and CP-violating effects are calculated for the upcoming NOvA and Hyper-K experiments.
The latest experimental progress have established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parametrizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi-Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase $delta_{rm CK}=(85.48^{+4.67(+12.87)}_{-1.80(-4.90)})^circ$ within $1sigma (3sigma)$ range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP-violation related measurements.
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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