Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction

Abstract

A nonperturbative Schwinger-Dyson analysis of mass generation is presented for a non-Hermitian PT-symmetric field theory in four dimensions of an axion coupled to a Dirac fermion.The model is motivated by phenomenological considerations.The axion has a quartic self-coupling $\lambda$ and a Yukawa coupling $g$ to the fermion. The Schwinger-Dyson equations are derived for the model with generic couplings. In the non-Hermitian case there is an additional nonperturbative contribution to the scalar mass. In a simplified rainbow analysis the solutions for the SD equations, are given for different regimes of the couplings $g$ and $\lambda$.

References in corpus (29)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermitian Representation of Quantum Mechanics
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Chern-Simons Modification of General Relativity
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• The ODE/IM Correspondence
• Solution of Schwinger-Dyson Equations for $\mathcal{P}\mathcal{T}$-Symmetric Quantum Field Theory
• Ghost Busting: PT-Symmetric Interpretation of the Lee Model
• Symmetries and conservation laws in non-Hermitian field theories
• The Fermionic Universal One-Loop Effective Action
• Anomalous Majorana Neutrino Masses from Torsionful Quantum Gravity
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories
• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• The disappearing $Q$ operator
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• Dynamical Majorana Neutrino Masses and Axions II: Inclusion of Axial Background and Anomaly Terms
• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• On the consistency of a non-Hermitian Yukawa interaction
• PT-symmetric interpretation of unstable effective potentials
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Dynamical Majorana Neutrino Masses and Axions
• Non-Hermitian gauge field theories and BPS limits
• Differential Renormalization of a Yukawa Model with ${\gamma }_5$
• PT-Symmetric Quantum Electrodynamics and Unitarity
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• A study of Schwinger-Dyson Equations for Yukawa and Wess-Zumino Models

Cited by in corpus (2)

• 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
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$