Massive and Massless Neutrinos on Unbalanced Seesaws

TL;DR

This paper explores a gauge theory extension with unbalanced seesaws, revealing that the number of massless neutrinos is an exact consequence of the model, independent of traditional approximations, and demonstrating a natural balance between massive neutrinos.

Contribution

It introduces a framework where the count of massless neutrinos is an inherent feature, not reliant on approximations, and clarifies the relationship between neutrino masses in unbalanced seesaw models.

Findings

Existence of (p-q) massless neutrinos is an exact result of the model.

The number of massive left- and right-handed neutrinos are balanced.

Illustration with the minimal seesaw model showing one massless neutrino.

Abstract

The observation of neutrino oscillations requires new physics beyond the standard model (SM). A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)_L x U(1)_Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix. Given p>q, the rank of M is in general equal to 2q, corresponding to 2q non-zero mass eigenvalues. The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M_\nu and the q x q heavy Majorana neutrino mass matrix M_R. In other words, the numbers of massive left- and right-handed neutrinos are fairly matched. A good example to illustrate this seesaw fair play rule is the minimal seesaw model with p=3 and q=2, in which one massless neutrino sits on the unbalanced seesaw.