The A4 flavor symmetry and neutrino phenomenology

TL;DR

This paper analyzes how the $A_4$ flavor symmetry affects neutrino mixing, exploring deviations from tribimaximal mixing due to Higgs VEV misalignments and identifying phenomenologically viable models.

Contribution

It provides a comprehensive analysis of neutrino mass matrices within the $A_4$ framework, including effects of Higgs VEV deviations and identifying conditions for exact tribimaximal mixing.

Findings

Deviations from tribimaximal mixing arise from Higgs VEV misalignments and extra singlet scalars.

Exact tribimaximal mixing requires fine-tuning and is generally disfavored by current data.

Certain neutrino mass matrices are strongly disfavored by experimental observations.

Abstract

It has been shown that tribimaximal mixing can be obtained by some particular breaking pattern of the $A_4$ symmetry, wherein the extra $A_4$ triplet Higgs scalars pick up certain fixed vacuum expectation value (VEV) alignments. We have performed a detailed analysis of the different possible neutrino mass matrices within the framework of the $A_4$ model. We take into account all possible singlet and triplet Higgs scalars which leave the Lagrangian invariant under $A_4$. We break $A_4$ spontaneously, allowing the Higgs to take any VEV in general. We show that the neutrino mixing matrix deviates from tribimaximal, both due to the presence of the extra Higgs singlets, as well as from the deviation of the triplet Higgs VEV from its desired alignment, taken previously. We solve the eigenvalue problem for a variety of these illustrative cases and identify the ones where one obtains exact tribimaximal mixing. All such cases require fine-tuning. We show which neutrino mass matrices would be strongly disfavored by the current neutrino data. Finally, we study in detail the phenomenology of the remaining viable mass matrices and establish the deviation of the neutrino mixing from tribimaximal, both analytically as well as numerically.