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, we first motivate physically such interactions, in the context of string-inspired low-energy effective field theories, involving right-handed neutrinos and axion fields. Then we proceed to discuss their formal consistency within the so-called Parity-Time-reversal(PT)-symmetry framework. Subsequently, we review 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.
Highlights
The Parity-Time-reversal(PT)-symmetry framework [1, 2, 3, 4] is an innovative approach to quantum theory, with a plethora of theoretical and experimental applications in various branches of physics PT symmetry guarantees the self consistency of quantum mechanical models with non-Hermitian Hamiltonians, characterised by real energy eigenvalues
If a quantum system is characterised by an antilinear symmetry, this is the most general condition that one can impose on a quantum theory for which one can have a time-independent inner product and a self-adjoint Hamiltonian with real energy eigenvalues
We would like to remark that in the absence of attractive four-fermion interactions, i.e. when g = 0, there is no dynamical mass generation for fermions, but there could be for axions φ(x) fields, as follows from energetics arguments [40] that we review in the subsection
Summary
The Parity-Time-reversal(PT)-symmetry framework [1, 2, 3, 4] is an innovative approach to quantum theory, with a plethora of theoretical and experimental applications in various branches of physics (for a partial but indicative list of such applications, which are rapidly expanding, though, to embrace new phenomena, even as this review is being written, the reader can consult the mini review [5].) PT symmetry guarantees the self consistency of quantum mechanical models with non-Hermitian Hamiltonians, characterised by real energy eigenvalues. As shown in [10], requiring the existence of time-independent inner products and invariance under complex Lorentz transformations, forces the antilinear symmetry to be uniquely CPT [10] In this way, the standard CPT theorem (with C denoting the standard Dirac charge-conjugation operator), which is based on locality, unitarity and Lorentz invariance of the corresponding field-theoretic Lagrangian densities, can be extended to appropriate field-theoretic systems with non-Hermitian Hamiltonians. The structure of the article is as follows: 2, we review the string-inspired model [43] and explain how the non-Hermitian Yukawa interactions emerge, along with nonHermitian anomalous couplings of the pseudoscalar (axion-like) fields We note at this point that the axion-like particles in this model are associated with stringy excitations and are in general different from the QCD axion.
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