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Register a new userBreaking of the tetra-maximal neutrino mixing pattern
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Newton Nath
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We make an attempt to study the present status of the tetra-maximal neutrino mixing (TMM) pattern. It predicts all the three leptonic mixing angles $theta_{13} approx 8.4^circ, theta_{12} approx 30.4^circ, $ and $theta_{23} = 45^circ $ together with the three CP-violating phases $ - delta = rho = sigma = 90^circ $. However, the latest global analysis of neutrino oscillation data prefer relatively higher best-fit value of $ theta_{12} $ as well as non-maximal values of both $ theta_{23}, delta $. In order to explain the realistic data, we study the breaking of TMM pattern. We first examine the breaking of TMM due to renormalization group (RG) running effects and then study the impact of explicit breaking terms. We also examine the effect of RG-induced symmetry breaking on the effective Majorana neutrino mass in neutrinoless double beta decay experiments.
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The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal, putting leptonic mixing in contrast with the small mixing of the quark sector. We discuss a model in which Delta(27) (a subgroup of SU(3)) is the family symmetry, and tri-bi-maximal mixing directly follows from the vacuum structure enforced by the discrete symmetry. The model accounts for the observed quark and lepton masses and the CKM matrix, as well as being consistent with an underlying stage of Grand Unification.
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.
We re-evaluate neutrino mixing patterns according to the latest T2K result for a larger mixing angle $theta_{13}$, and find that the PMNS mixing matrix has larger deviations from bimaximal (BM) and tribimaximal (TB) mixing patterns than previously expected. We also find that several schemes connecting PMNS and CKM mixing matrices can accommodate the latest T2K result nicely. As necessary updates to former works, we make new triminimal expansions of PMNS mixing matrix based on BM and TB mixing patterns. We also propose a new mixing pattern with a self-complementary relation between the mixing angles $theta_{12}^{ u} + theta_{13}^{ u} simeq 45^circ$, and find such a new mixing pattern in leading order can provide a rather good description of the data.
The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. We argue that this structure suggests a family symmetric origin in which the magnitude of the mixing angles are related to the existence of a discrete non-Abelian family symmetry. We construct a model in which the family symmetry is the non-Abelian discrete group $Delta(27)$, a subgroup of SU(3) in which the tri-bi-maximal mixing directly follows from the vacuum structure enforced by the discrete symmetry. In addition to the lepton mixing angles, the model accounts for the observed quark and lepton masses and the CKM matrix. The structure is also consistent with an underlying stage of Grand Unification.
I propose a model of radiative charged-lepton and neutrino masses with $A_4$ symmetry. The soft breaking of $A_4$ to $Z_3$ lepton triality is accomplished by dimension-three terms. The breaking of $Z_3$ by dimension-two terms allow cobimaximal neutrino mixing $(theta_{13} eq 0, theta_{23} = pi/4, delta_{CP} = pm pi/2)$ to be realized with only very small finite calculable deviations from the residual lepton triality. This construction solves a long-standing technical problem inherent in renormalizable $A_4$ models since their inception.
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