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.

7 pages, comments added

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• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Non-Hermiticity: a new paradigm for model building in particle physics