Analytic structure of scalar composites in the symmetric phase of the gauged Nambu-Jona-Lasinio model

TL;DR

This paper analyzes the analytic structure of scalar composites in the symmetric phase of the gauged Nambu-Jona-Lasinio model, revealing their behavior near the critical scaling region and deriving an analytic scalar propagator.

Contribution

It introduces a method to solve the Schwinger-Dyson equation for the Yukawa vertex, enabling an analytic expression for the scalar propagator along the critical curve.

Findings

Scalar composites become relevant at short distances near criticality

An analytic scalar propagator valid along the entire critical curve is derived

The mass and width of scalar composites are reexamined in the critical region

Abstract

The gauged Nambu-Jona-Lasinio model in the quenched-ladder approximation has non-trivial dynamics near a critical scaling region (critical curve) separating a chiral symmetric and a dynamically chiral symmetry broken phase. Scalar and pseudoscalar composites corresponding to the four-fermion interaction become relevant degrees of freedom at short distances, which is reflected in the appearance of a large anomalous dimension of the four-fermion operators. A method is introduced for solving the Schwinger-Dyson equation for the Yukawa vertex in specific kinematic regimes. This allows one to derive an analytic expression for the scalar propagator, which is valid along the entire critical curve. The mass and width of the scalar composites in the critical scaling region are reexamined and the conformal phase transition at the critical gauge coupling is discussed.