  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.
