Bottom-up approach to texture zeros in the neutrino mass matrix

TL;DR

This paper uses a bottom-up approach to analyze possible texture zeros in the neutrino mass matrix, considering current oscillation data, and identifies which matrix elements can vanish for different neutrino mass orderings.

Contribution

It provides a detailed analysis of texture zeros in the neutrino mass matrix using the latest data, highlighting allowed zero elements and correlations with CP phases and neutrino mass.

Findings

Certain matrix elements can vanish depending on mass ordering.

Allowed two-zero textures are identified for normal ordering.

Strong correlations between CP phases and the lowest neutrino mass are found.

Abstract

We investigate one and two texture zeros in the neutrino mass matrix using the latest oscillation data through a bottom-up approach. In this context, we begin by estimating the detailed features of each matrix element by varying the CP violating phases within $(0,\,2\pi)$, the lowest neutrino mass within $(0,\,1)\,{\rm eV}$ and the neutrino oscillation parameters such as three mixing angles and the two mass squared differences within $3\sigma$ of their central values. We find that for normal ordering, only $ee$, $e\mu$ and $e\tau$ elements of the mass matrix can vanish, whereas, for inverted ordering, five elements -- $e\mu$, $e\tau$, $\mu\mu$, $\mu\tau$ and $\tau\tau$ -- can vanish. For two texture zeros, only $(ee,\, e\mu = 0)$ and $(ee,\, e\tau =0)$ are allowed in case of normal ordering. For a particular vanishing element, we also estimate the range of the lowest neutrino mass and the CP violating phases. In particular, very interesting correlation among the CP violating phases and the lowest neutrino mass is obtained for each vanishing cases.