Gauge Independent Phase Structure of Gauged Nambu-Jona-Lasinio and Yukawa Models

TL;DR

This paper studies the phase transition behavior of gauged NJL and Yukawa models using a gauge-invariant method, revealing critical lines and exponents that are independent of gauge choice and consistent with mean-field theory.

Contribution

It introduces a gauge-invariant inversion method to analyze critical behavior, deriving critical lines and exponents for gauged NJL and Yukawa models, ensuring gauge independence.

Findings

Critical lines separating phases are derived.

Chiral phase transition exhibits mean-field critical exponents.

Results are gauge-parameter independent and consistent with previous Schwinger-Dyson analyses.

Abstract

We investigate the critical behavior of the gauged NJL model (QED plus 4-fermion interaction) and the gauged Yukawa model by use of the inversion method. By calculating the gauge-invariant chiral condensate in the inversion method to the lowest order, we derive the critical line which separates the spontaneous chiral-symmetry breaking phase from the chiral symmetric one. The critical exponent for the chiral order parameter associated with the second order chiral phase transition is shown to take the mean-field value together with possible logarithmic correction to the mean-field prediction. All the above results are gauge-parameter independent and are compared with the previous results obtained from the Schwinger-Dyson equation for the fermion propagator.