Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction

TL;DR

This paper investigates nonperturbative mass generation in a four-dimensional non-Hermitian PT-symmetric axion-fermion model using Schwinger-Dyson equations, revealing additional contributions to scalar mass from non-Hermitian effects.

Contribution

It derives Schwinger-Dyson equations for a PT-symmetric axion-fermion theory and analyzes nonperturbative mass generation, including effects unique to non-Hermitian interactions.

Findings

Additional nonperturbative scalar mass contributions in the non-Hermitian case

Solutions for Schwinger-Dyson equations across different coupling regimes

Insights into mass generation mechanisms in PT-symmetric field theories

Abstract

A nonperturbative Schwinger-Dyson analysis of mass generation is presented for a non-Hermitian PT-symmetric field theory in four dimensions of an axion coupled to a Dirac fermion.The model is motivated by phenomenological considerations.The axion has a quartic self-coupling $\lambda$ and a Yukawa coupling $g$ to the fermion. The Schwinger-Dyson equations are derived for the model with generic couplings. In the non-Hermitian case there is an additional nonperturbative contribution to the scalar mass. In a simplified rainbow analysis the solutions for the SD equations, are given for different regimes of the couplings $g$ and $\lambda$.