Explicit chiral symmetry breaking and the 1/N expansion in models with multi-fermion interactions

TL;DR

This paper discusses how to correctly perform the 1/N expansion in multi-fermion models with explicit chiral symmetry breaking, ensuring the original symmetry breaking pattern is preserved during calculations.

Contribution

It provides a consistent method for integrating over quark fields in models with explicit chiral symmetry breaking, maintaining the original symmetry breaking pattern.

Findings

A method to handle the fermion determinant without altering symmetry breaking

Clarification on the 1/N expansion in multi-fermion models

Ensuring the symmetry breaking pattern remains intact during calculations

Abstract

Explicit chiral symmetry breaking is a natural feature of many QCD inspired models with multi-quark interactions. To carry out the 1/N expansion of these theories, one integrates over the quark fields. In the process of calculating the one-loop fermion determinant which is not chiral invariant due to quark masses, special care must be taken in order not to alter the original symmetry breaking pattern of the Lagrangian. We show how to do this consistently.