On the consistency of a non-Hermitian Yukawa interaction

Abstract

We study different properties of an anti-Hermitian Yukawa interaction, motivated by a scenario of radiative anomalous generation of masses for the right-handed sterile neutrinos. The model, involving either a pseudo-scalar or a scalar, is consistent both at the classical and quantum levels, and particular attention is given to its properties under improper Lorentz transformations. The path integral is consistently defined with a Euclidean signature, and we discuss the energetics of the model, which show that no dynamical mass generation can occur, unless extra interactions are considered.

arXiv comment7 pages, comments added

References in corpus (15)

• General relativity as an effective field theory: The leading quantum corrections
• The type IIB string axiverse and its low-energy phenomenology
• Introduction to PT-Symmetric Quantum Theory
• Dual PT-Symmetric Quantum Field Theories
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• Symmetries and conservation laws in non-Hermitian field theories
• Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
• Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
• Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories
• Anomalous Majorana Neutrino Masses from Torsionful Quantum Gravity
• Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• Infinitely many inequivalent field theories from one Lagrangian
• Decay of the Higgs boson to ${\tau }^{-}{\tau }^{+}$ and non-Hermiticity of the Yukawa interaction

Cited by in corpus (18)

• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Dynamical Majorana Neutrino Masses and Axions II: Inclusion of Axial Background and Anomaly Terms
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Dynamical Majorana Neutrino Masses and Axions
• Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• The phase diagram and vortex properties of PT-symmetric non-Hermitian two-component superfluid
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Non-Hermiticity: a new paradigm for model building in particle physics
• 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
• Neutrino mass observables and non-Hermitian version of Type-I seesaw model