The hidden symmetries in the PMNS matrix and the light sterile neutrino(s)

TL;DR

This paper investigates how the presence of a light sterile neutrino can explain deviations from symmetric textures in the PMNS matrix, suggesting a mechanism for symmetry breaking consistent with experimental data.

Contribution

It proposes that a light sterile neutrino can account for the observed deviations from symmetric PMNS textures, specifically addressing the disappearance of $$ symmetry.

Findings

Introducing one sterile neutrino partially restores symmetry.

A slight $$ symmetry breaking is necessary for data consistency.

The modified PMNS matrix aligns with experimental measurements within tolerance.

Abstract

The approximately symmetric form of the PMNS matrix suggests that there could exist a hidden symmetry which makes the PMNS matrix different from the CKM matrix for quarks. In literature, all the proposed fully symmetric textures exhibit an explicit $\mu-\tau$ symmetry in addition to other symmetries which may be different for various textures. Observing obvious deviations of the practical PMNS matrix elements from those in the symmetric textures, there must be a mechanism to distort the symmetry. It might be due to existence of light sterile neutrinos. In this work, we study the case of the Tribimaximal texture and propose that its apparent symmetry disappears due to existence of a sterile neutrino. We observe that introducing just one sterile neutrino is still not sufficient to recover the data, thus a slight $\mu-\tau$ symmetry breaking is also needed. By considering those factors, we obtain the PMNS matrix elements which are consistent with data within the experimental tolerance.