A modified Friedberg-Lee symmetry for the TM1 neutrino mixing

TL;DR

This paper introduces a modified Friedberg-Lee symmetry for neutrino mass matrices that naturally leads to the TM1 mixing pattern, aligning better with experimental data and allowing for a massless neutrino state.

Contribution

The paper proposes a modified FL symmetry that results in the TM1 neutrino mixing pattern, improving upon the original FL symmetry's predictions and maintaining symmetry without breaking.

Findings

Modified FL symmetry yields TM1 mixing consistent with experiments.

Allows for a massless neutrino state ($m_1=0$).

Discusses combination with $bc$ reflection symmetry.

Abstract

In this letter, we put forward a special neutrino mass matrix which is invariant under a modified Friedberg-Lee (FL) transformation $\nu^{}_e \to \nu^{}_e-2\theta$ and $\nu^{}_{\mu, \tau} \to \nu^{}_{\mu, \tau}+\theta$ with $\theta$ being a space-time independent element of the Grassmann algebra. Compared to the original FL symmetry (with the transformation $\nu^{}_{e, \mu, \tau} \to \nu^{}_{e, \mu, \tau}+\theta$) which results in the TM2 neutrino mixing, the modified FL symmetry will lead us to the TM1 mixing which has a better agreement with the experimental results. While the original FL symmetry has to be broken in order to produce a realistic neutrino mass spectrum, the modified FL symmetry is allowed to remain intact and give us a vanishing $m^{}_1$. A combination of the FL symmetry with the $\mu$-$\tau$ reflection symmetry is also discussed.