The high temperature CP-restoring phase transition at theta = pi

TL;DR

This paper compares the CP-restoring phase transition at theta = pi at high temperature using NJL and linear sigma models, revealing that a non-analytic vacuum term in NJL models crucially influences the transition's nature.

Contribution

It identifies the impact of a non-analytic vacuum term in the NJL model on the order of the CP-restoring phase transition at high temperature.

Findings

NJL model predicts a different transition order than the linear sigma model.

The non-analytic vacuum term is key to the transition's qualitative behavior.

Absence of explicit CP violation affects the phase transition characteristics.

Abstract

The CP-restoring phase transition at theta = pi and high temperature is investigated using two related models that aim to describe the low-energy phenomenology of QCD, the NJL model and the linear sigma model coupled to quarks. Despite many similarities between the models, different predictions for the order of the phase transition result. Using the Landau-Ginzburg formalism, the origin of this difference is traced back to a non-analytic vacuum term at zero temperature that is present in the NJL model, but usually not included in the linear sigma model. Due to the absence of explicit CP violation, this term always alters the qualitative aspects of the high temperature phase transition at theta = pi, just as for theta = 0 in the chiral limit.