Mass protection via translational invariance

TL;DR

This paper introduces a novel mechanism leveraging translational invariance to protect Dirac fermions from acquiring mass, potentially explaining small neutrino masses without fine-tuning, and demonstrates its feasibility on the lattice.

Contribution

It presents a new symmetry-based approach to prevent fermion mass generation, applicable to neutrinos, and shows how to implement it in lattice formulations.

Findings

The mechanism forbids the Yukawa coupling for neutrinos.

It can be realized in lattice theories.

It offers a potential explanation for small neutrino masses.

Abstract

We propose a way of protecting a Dirac fermion interacting with a scalar field from acquiring a mass from the vacuum. It is obtained through an implementation of translational symmetry when the theory is formulated with a momentum cutoff, which forbids the usual Yukawa term. We consider that this mechanism can help to understand the smallness of neutrino masses without a tuning of the Yukawa coupling. The prohibition of the Yukawa term for the neutrino forbids at the same time a gauge coupling between the right-handed electron and neutrino. We prove that this mechanism can be implemented on the lattice.