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

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.

24 pages revtex, eight figures incorporated. In this version, a brief discussion has been added in the introduction, on the justification of ignoring perturbative string-inspired axion-like particle potentials, and also in the conclusions on a comparison of the magnitude of the dynamical mass with ordinary QCD axion masses. No effects on conclusions

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• Renormalisation group flows connecting a $4-\epsilon$ dimensional Hermitian field theory to a $\mathcal{P}\mathcal{T}$-symmetric theory for a fermion coupled to an axion
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