Dynamical Majorana Neutrino Masses and Axions

Abstract

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, 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. The situation is opposite for an anti-Hermitian Yukawa model: there is (pseudo)scalar dynamical mass generation, but no fermion dynamical mass generation.In the presence of additional attractive four-fermion interactions, dynamical fermion mass generation can occur in these models, under appropriate conditions and range of their couplings.

24 pages revtex, one eps figure incorporated; section IIIC contains material related to arXiv:2004.03699 [hep-ph]. Minor restructuring on sections, with section II added. Also discussion added, along with Figure 2 and ref. [25], on resummation of four-fermion loops, which justifies our approximations. Minor typos corrected. No effects on conclusions. Version to be published in Nuclear Physics B

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• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Decay of the Higgs boson $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\nu }_{\tau }{\pi }^{+}{\bar{\nu }}_{\tau }$ for a non-Hermitian Yukawa interaction
• Thermodynamic properties of non-Hermitian Nambu--Jona-Lasinio models