Dynamical Majorana Neutrino Masses and Axions

We discuss dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in the context of effective theories containing Yukawa type interactions between the fermions and ALPs. We discuss both Hermitian and non-Hermitian Yukawa interactions, which are motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in some effective field theories. The latter contain shift-symmetry breaking Yukawa interactions between sterile neutrinos and ALPs. We show that, unless additional interactions are included, dynamical fermion mass generation cannot occur in these models, but axion mass can be generated dynamically only in the Hermitian Yukawa interaction case. Additional attractive four fermion interactions, that may exist in string-inspired multi-axion effective field theories, can lead to dynamical-fermion-mass generation in both Hermitian and anti-Hermitian models, for appropriate ranges of their couplings.