Knitting neutrino mass textures with or without Tri-Bi maximal mixing

TL;DR

This paper explores the underlying symmetries of neutrino mass textures and mixing matrices, deriving analytical relations and proposing minimal extensions to explain observed neutrino oscillation data.

Contribution

It provides exact analytical expressions linking neutrino and charged lepton parameters to experimental data and introduces minimal modifications to existing mixing matrices.

Findings

Derived exact relations between mass and mixing parameters.

Identified constraints on neutrino mixing models.

Proposed minimal extensions to Tri-Bi maximal mixing matrices.

Abstract

The solar and baseline neutrino oscillation data suggest bimaximal neutrino mixing among the first two generations, and trimaximal mixing between all three neutrino flavors. It has been conjectured that this indicates the existence of an underlying symmetry for the leptonic fermion mass textures. The experimentally measured quantities however, are associated to the latter indirectly and in a rather complicated way through the mixing matrices of the charged leptons and neutrinos. Motivated by these facts, we derive exact analytical expressions which directly link the charged lepton and neutrino mass and mixing parameters to measured quantities and obtain constraints on the parameter space. We discuss deviations from Tri-Bi mixing matrices and present minimal extensions of the Harrison Perkins and Scott matrices capable of interpreting all neutrino data.