Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation

Abstract

In this mini review, we discuss some recent developments regarding properties of (quantum) field-theory models containing anti-Hermitian Yukawa interactions between pseudoscalar fields (axions) and Dirac (or Majorana) fermions. Specifically, after motivating physically such interactions, in the context of string-inspired low-energy effective field theories, involving right-handed neutrinos and axion fields, we proceed to discuss their formal consistency within the so-called Parity-Time-reversal(PT)-symmetry framework, as well as dynamical mass generation, induced by the Yukawa interactions, for both fermions and axions. The Yukawa couplings are assumed weak, given that they are conjectured to have been generated by non-perturbative effects in the underlying microscopic string theory. The models under discussion contain, in addition to the Yukawa terms, also anti-Hermitian anomalous derivative couplings of the pseudoscalar fields to axial fermion currents, as well as interactions of the fermions with non-Hermitian axial backgrounds. We discuss the role of such additional couplings on the Yukawa-induced dynamically-generated masses. For the case where the fermions are right-handed neutrinos, we compare such masses with the radiative ones induced by both, the anti-Hermitian anomalous terms and the anti-Hermitian Yukawa interactions in phenomenologically relevant models.

35 pages latex, 2 figures. Review based on talk in the online series: Pseudo-Hermitian Hamiltonians in Quantum Physics (XIX<vPHHQP<XX), partially based on works appeared in arXiv:2004.03699 (Phys. Lett. B), arXiv:2004.04611 (Nucl. Phys. B) and arXiv:2006.13616. Submitted for publication to the Proc. (eds. C.M. Bender, F. Correa and A. Fring, Journal of Physics: Conference Series (IoP Publishing))

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Cited by in corpus (5)

• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions
• Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction
• 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
• Decay of the Higgs boson $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\nu }_{\tau }{\pi }^{+}{\bar{\nu }}_{\tau }$ for a non-Hermitian Yukawa interaction