Chiral Symmetry in Dirac Equation and its Effects on Neutrino Masses and Dark Matter

TL;DR

This paper incorporates chiral symmetry into the Dirac equation to explain small neutrino masses and propose a new dark matter candidate, linking fundamental symmetries to particle physics phenomena.

Contribution

It introduces a novel approach to include chiral symmetry in the Dirac equation using Poincaré group representations, leading to new insights on neutrino masses and dark matter.

Findings

Chiral symmetry explains small neutrino masses.

Predicts a new massive dark matter particle candidate.

Provides a basis for further experimental verification.

Abstract

Chiral symmetry is included into the Dirac equation using the irreducible representations of the Poincar\'e group. The symmetry introduces the chiral angle that specifies the chiral basis. It is shown that the correct identification of these basis allows explaining small masses of neutrinos and predicting a new candidate for Dark Matter massive particle.