Modified perturbation theory for the Yukawa model

TL;DR

This paper introduces a modified perturbation theory for the Yukawa model using a self-consistent field approach, revealing conditions under which fermions gain mass through scalar interactions, relevant to neutrino mass discussions.

Contribution

It proposes a new perturbation framework for the Yukawa model based on a self-consistent field approximation, enabling analysis of fermion mass generation.

Findings

Fermions can acquire mass via scalar exchange only if the coupling exceeds a critical value.

The approach leads to a normally ordered interaction Hamiltonian.

Implications for neutrino mass are discussed.

Abstract

A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for the effects caused by the interaction of fields. Such choice of the main approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of the fermion mass due to the interaction with exchange of the scalar boson is investigated. It is demonstrated that, for zero bare mass, the fermion can acquire mass only if the coupling constant exceeds the critical value determined by the boson mass. In this connection, the problem of the neutrino mass is discussed.