Flavor Neutrino Masses giving sin\theta_{13}=0

TL;DR

This paper explores how specific conditions on flavor neutrino mass matrices can naturally lead to a vanishing reactor mixing angle, , providing insights into neutrino mixing models consistent with experimental observations.

Contribution

It derives explicit conditions on neutrino mass matrix elements that result in =0, linking phase relations and mass matrix constraints to neutrino mixing parameters.

Findings

Conditions on M_{e} and M_{ au au} lead to =0

Rephasing invariance determines phase relations

Provides a framework for neutrino mixing models with =0

Abstract

Among neutrino mixings, the reactor mixing angle, \theta_{13}, is observed to be almost vanishing and is consistent with \theta_{13}=0. We discuss how the condition of \theta_{13}=0 constrains models of neutrino mixings and show that, for flavor neutrino masses given by M_{ij} (i,j=e,\mu,\tau), two conditions of M_{e\tau}=-e^{2i\gamma}tan(\theta_{23})M_{e\mu} and M_{\tau\tau}=e^{4i\gamma}M_{\mu\mu}+e^{2i\gamma}[2/tan(2\theta_{23})]M_{\mu\tau} lead to \theta_{13}=0, where \theta_{23} is the atmospheric neutrino mixing angle and \gamma is its associated phase. The rephasing invariance can select two phases provided by \alpha=arg(M_{e\mu}) and \beta=arg(M_{e\tau}), giving \gamma=(\beta-\alpha)/2.