Effective quark Lagrangian in the instanton-gas model

TL;DR

This paper derives a nonlocal NJL-type effective quark Lagrangian within the dilute instanton gas model, capturing multi-quark interactions and connecting with existing literature on topologically neutral chiral symmetry breaking.

Contribution

It provides a straightforward derivation of a nonlocal effective quark Lagrangian with multi-quark vertices in the instanton-gas framework, clarifying its relation to prior results.

Findings

Derivation of a nonlocal NJL-type Lagrangian with multi-quark vertices

Establishment of correspondence with previous literature

Analysis within the topologically neutral chiral broken phase

Abstract

A straightforward derivation of the effective quark Lagrangian is presented for the topologically neutral chiral broken phase of the dilute instanton gas. The resulting quark Lagrangian is a nonlocal NJL-type and contains 4q, 6q,... vertices for any number of flavours. Correspondence of this result with previously known in literature is discussed in detail.