Dynamical Majorana Neutrino Masses and Axions II: Inclusion of Axial Background and Anomaly Terms

TL;DR

This paper investigates how anomaly terms and axial backgrounds influence dynamical mass generation for fermions and axion-like particles in theories relevant to neutrino physics and early Universe scenarios, revealing conditions under which masses are generated or suppressed.

Contribution

It extends previous models by including anomaly and axial background effects, analyzing their impact on fermion and scalar mass generation in Yukawa-interacting theories.

Findings

Hermitian Yukawa interactions lead to fermion mass generation with scalar mass addition.

Anomaly terms can induce fermion masses similar to four-fermion interactions.

Axial backgrounds enhance or suppress mass generation depending on interaction Hermiticity.

Abstract

We extend the study of a previous publication \cite{amsot} on Schwinger-Dyson dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in field theories containing Yukawa type interactions between the fermions and ALPs, by incorporating anomaly terms and/or (constant) axial background fields. The latter are linked to some Lorentz (and CPT) violating scenarios for leptogenesis in the early Universe. We discuss both Hermitian and non-Hermitian Yukawa interactions, anomaly terms and axial backgrounds, which are all motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in string-isnpired, low-energy, effective field theories, including attractive four-fermion interactions. We show that, for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynamical mass generation, but there is fermion dynamical mass generation, provided one adds a bare (pseudo)scalar mass. For this case, the hermitian anomaly terms play a similar role in inducing dynamical mass generation for fermions as the four-fermion attractive interactions. For antihermitian Yukawa interactions, an antihermitian anomaly resists mass generation. The axial background terms assist dynamical mass generation induced by antihermitian Yukawa interactions, in the sense that the larger the magnitude of the background, the larger the dynamical mass. For hermitian Yukawa interactions, however, the situation is the opposite, in the sense that the larger the background the smaller the dynamical mass. We also compare the anomaly-induced dynamical mass with the radiative fermion mass in models of sterile neutrinos, and find that in cases where the dynamical mass occurs, the latter dominates over the anomalously generated radiative sterile-neutrino mass.