Dynamical Majorana neutrino masses and axions II: Inclusion of anomaly terms and axial background

Abstract

We extend the study of a previous publication [1] 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 and axial backgrounds, which are motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in some effective field theories, including attractive four-fermion interactions. The reality requirement for the radiative, anomalously generated, mass component for the fermions, restricts our considerations to the cases where Yukawa interactions and the anomaly terms are either both Hermitian or both anti-Hermitian. 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 rôle in inducing dynamical mass generation for fermions as the four-fermion attractive interactions, and as such they can themselves generate a small dynamical mass. For anti-Hermitian Yukawa interactions, an anti-Hermitian anomaly resists mass generation. The axial background terms assist dynamical mass generation induced by anti-Hermitian 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.