Symmetry breaking via fermion 4-point functions

TL;DR

This paper develops a framework for analyzing nonperturbative fermion 4-point functions, revealing new insights into symmetry breaking mechanisms relevant to high-energy flavor interactions.

Contribution

It introduces the effective action and gap equations for fermion 4-point functions, highlighting differences from 2-point functions and limitations of gauge exchanges in certain regimes.

Findings

Gauge exchanges cannot generate nonperturbative 4-point functions at large color numbers.

The structure of gap equations for 4-point functions differs from naive 2-point generalizations.

Applicable to theories with massless fermions above the electroweak scale.

Abstract

We construct the effective action and gap equations for nonperturbative fermion 4-point functions. Our results apply to situations in which fermion masses can be ignored, which is the case for theories of strong flavor interactions involving standard quarks and leptons above the electroweak scale. The structure of the gap equations is different from what a naive generalization of the 2-point case would suggest, and we find for example that gauge exchanges are insufficient to generate nonperturbative 4-point functions when the number of colors is large.