# Alternative formulation of left-right symmetry with $B-L$ conservation and purely Dirac neutrinos

## TL;DR

This paper introduces a novel Left-Right Symmetric Model where $B-L$ remains a global symmetry, leading to purely Dirac neutrinos and avoiding $B-L$ violation, with neutrino masses generated via radiative or seesaw mechanisms.

## Contribution

It presents an alternative formulation of LRSM with unbroken $B-L$ symmetry, enabling Dirac neutrino masses and explaining the absence of $B-L$ violation.

## Key findings

- Neutrino masses are purely Dirac type.
- $B-L$ remains a global symmetry after symmetry breaking.
- Neutrino masses generated via two-loop radiative or Dirac seesaw mechanisms.

## Abstract

We propose an alternative formulation of a Left-Right Symmetric Model (LRSM) where the difference between baryon number ($B$) and lepton number ($L$) remains an unbroken symmetry. This is unlike the conventional formulation, where $B-L$ is promoted to a local symmetry and is broken explicitly in order to generate Majorana neutrino masses. In our case $B-L$ remains a global symmetry after the left-right symmetry breaking, allowing only Dirac mass terms for neutrinos. In addition to parity restoration at some high scale, this formulation provides a natural framework to explain $B-L$ as an anomaly-free global symmetry of the Standard Model and the non-observation of $(B-L)$-violating processes. Neutrino masses are purely Dirac type and are generated either through a two loop radiative mechanism or by implementing a Dirac seesaw mechanism.