Dirac or Inverse Seesaw Neutrino Masses with $B-L$ Gauge Symmetry and $S_3$ Flavour Symmetry

TL;DR

This paper explores alternative anomaly-free $B-L$ gauge symmetry models that enable Dirac or inverse seesaw neutrino masses, incorporating $S_3$ flavor symmetry to address neutrino mixing.

Contribution

It introduces new anomaly-free $B-L$ models supporting Dirac or inverse seesaw mechanisms, expanding beyond the traditional Majorana seesaw framework.

Findings

Identifies alternative anomaly-free $B-L$ solutions for neutrino masses.

Demonstrates application of $S_3$ flavor symmetry to neutrino mixing.

Provides theoretical framework for Dirac/inverse seesaw in $B-L$ models.

Abstract

Many studies have been made on extensions of the standard model with $B-L$ gauge symmetry. The addition of three singlet (right-handed) neutrinos renders it anomaly-free. It has always been assumed that the spontaneous breaking of $B-L$ is accomplished by a singlet scalar field carrying two units of $B-L$ charge. This results in a very natural implementation of the Majorana seesaw mechanism for neutrinos. However, there exists in fact another simple anomaly-free solution which allows Dirac or inverse seesaw neutrino masses. We show for the first time these new possibilities and discuss an application to neutrino mixing with $S_3$ flavour symmetry.