Minimal Modification to Tri-bimaximal Mixing

TL;DR

This paper investigates minimal modifications to the tri-bimaximal neutrino mixing matrix, introducing at most one new angle and phase, with some modifications aligning with recent experimental hints of non-zero θ13 and constraining CP violation.

Contribution

It systematically explores minimal modifications to the tri-bimaximal mixing matrix, identifying cases with testable predictions and constraints from recent neutrino oscillation data.

Findings

Certain minimal modifications are consistent with non-zero θ13.

Some modifications constrain the CP phase δ near 0 or π.

Experimental data sharply restrict possible CP violation phases.

Abstract

We explore some ways of minimally modifying the neutrino mixing matrix from tribimaximal, characterized by introducing at most one mixing angle and a CP violating phase thus extending our earlier work. One minimal modification, motivated to some extent by group theoretic considerations, is a simple case with the elements $V_{\alpha 2}$ of the second column in the mixing matrix equal to $1/\sqrt{3}$. Modifications by keeping one of the columns or one of the rows unchanged from tri-bimaximal mixing all belong to the class of minimal modification. Some of the cases have interesting experimentally testable consequences. In particular, the T2K and MINOS collaborations have recently reported indications of a non-zero $\theta_{13}$. For the cases we consider, the new data sharply constrain the CP violating phase angle $\delta$, with $\delta$ close to 0 (in some cases) and $\pi$ disfavored.