Non-Hermitian extension of gauge theories and implications for neutrino physics

TL;DR

This paper explores a non-Hermitian extension of gauge theories, specifically QED, introducing complex mass terms and couplings, which could explain neutrino mass smallness and CP violation.

Contribution

It develops a non-Hermitian gauge theory framework that maintains gauge invariance and offers new insights into neutrino physics and leptonic CP violation.

Findings

Gauge invariance restored when Hermitian and anti-Hermitian masses are equal

Model explains small neutrino masses

Provides an additional source of leptonic CP violation

Abstract

An extension of QED is considered in which the Dirac fermion has both Hermitian and anti-Hermitian mass terms, as well as both vector and axial-vector couplings to the gauge field. Gauge invariance is restored when the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory reduces to that of a single massless Weyl fermion. An analogous non-Hermitian Yukawa theory is considered, and it is shown that this model can explain the smallness of the light-neutrino masses and provide an additional source of leptonic CP violation.