Dynamical quark mass generation

TL;DR

This paper explores how a non-perturbative fermion mass can arise from spontaneous chiral symmetry breaking in lattice QCD-like theories, especially when coupled with a scalar field, leading to naturally light fermions.

Contribution

It demonstrates a mechanism for dynamical fermion mass generation involving scalar fields and Yukawa interactions, extending lattice QCD insights.

Findings

A non-perturbative fermion mass can be generated dynamically.

The mass is naturally light and independent of scalar field expectation value.

A critical Yukawa coupling enhances symmetry and mass generation.

Abstract

Taking inspiration from lattice QCD results, we argue that a non-perturbative mass term for fermions can be generated as a consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn triggered by the explicitly breaking of chiral symmetry induced by the critical Wilson term in the action. In a pure lattice QCD-like theory this mass term cannot be separated from the unavoidably associated linearly divergent contribution. However, if QCD with a Wilson term is enlarged to a theory where also a scalar field is present, coupled to a doublet of SU(2) fermions via a Yukawa interaction, then in the phase where the scalar field takes a non-vanishing (large) expectation value, a dynamically generated and ``naturally'' light fermion mass (numerically unrelated to the expectation value of the scalar field) is seen to emerge, at a critical value of the Yukawa coupling where the symmetry of the model is maximally enhanced.