High temperature CP-restoring phase transition at theta = pi

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 Nambu-Jona-Lasinio (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 nonanalytic vacuum term at zero temperature that is present in the NJL model, but usually not included in the linear sigma model. Because of 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.