Implication of a vanishing element in 3+1 Scenario

TL;DR

This paper investigates the conditions under which elements of the neutrino mass matrix vanish in a 3+1 neutrino model, analyzing the implications of sterile neutrinos and current experimental bounds.

Contribution

It provides a detailed analysis of zero textures in the neutrino mass matrix within the 3+1 scheme considering sterile neutrinos and current oscillation data.

Findings

Active-active mass matrix elements can vanish in allowed parameter space.

Active-sterile elements $m_{es}$ and $m_{ul s}$ can be small only for quasi-degenerate neutrinos.

Sterile-only element $m_{ss}$ remains around 1 eV across parameter space.

Abstract

In this paper we study the phenomenological implications of the one zero textures of low energy neutrino mass matrices in presence of a sterile neutrino. We consider the 3+1 scheme and use the results from global fit for short baseline neutrino oscillation data which provides the bounds on the three additional mixing angles. We find that the mass matrix elements $m_{\alpha \beta}$ ($\alpha, \beta = e, \mu, \tau$) involving only the active states can assume vanishing values in the allowed parameter space for all the mass spectrum. Among the mass matrix elements connecting the active and sterile states, $m_{es}$ and $m_{\mu s}$ can become small only for the quasi-degenerate neutrinos. The element $m_{\tau s}$ on the other hand can vanish even for lower values of masses since the 3-4 mixing angle only has an upper bound from current data. The mass matrix element ($m_{ss}$) involving only the sterile state stays $\sim$ $\mathcal{O}$(1) eV in the whole parameter region. We study the possible correlations between the sterile mixing angles and the Majorana phases to give a zero element in the mass matrix.