On the dynamical breaking of chiral symmetry: a new mechanism

TL;DR

This paper introduces a new mechanism where higher-derivative terms in a U(1) gauge theory induce chiral symmetry breaking at low energies, leading to fermion mass generation in weak coupling regimes.

Contribution

It demonstrates that higher-derivative gauge terms can trigger chiral symmetry breaking and fermion mass generation, extending the mechanism to non-Abelian theories and massive gauge fields.

Findings

Higher-derivative terms induce chiral symmetry breaking at low energy.

Fermion mass depends on energy scale and gauge coupling non-perturbatively.

Extensions to SU(N) and massive gauge fields analyzed.

Abstract

We consider a U(1) gauge theory, minimally coupled to a massless Dirac field, where a higher-derivative term is added to the pure gauge sector, as in the Lee-Wick models. We find that this term can trigger chiral symmetry breaking at low energy in the weak coupling regime. Then, the fermion field acquires a mass that turns out to be a function of both the energy scale associated to the higher-derivative term and the gauge coupling. The dependence of the fermion mass on the gauge coupling is non-perturbative. Extensions to SU(N) gauge theories and fermion-scalar interactions are also analyzed, as well as to theories with massive gauge fields. A few implications of these results in the framework of quark-mass generation are discussed.