Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method

TL;DR

This paper investigates chiral symmetry restoration in linear and nonlinear O(N) models using an auxiliary field approach, analyzing phase transition orders and meson properties at finite temperature within the CJT formalism.

Contribution

It demonstrates the equivalence of the auxiliary field method to the standard models up to two-loop order and explores the impact of renormalization schemes on phase transition nature.

Findings

The effective potentials of both models are identical up to two-loop order.

The order of the chiral phase transition varies with the model type and parameters.

Goldstone's theorem remains valid in the physical parameter space.

Abstract

We consider the O(N) linear {\sigma} model and introduce an auxiliary field to eliminate the scalar self-interaction. Using a suitable limiting process this model can be continuously transformed into the nonlinear version of the O(N) model. We demonstrate that, up to two-loop order in the CJT formalism, the effective potential of the model with auxiliary field is identical to the one of the standard O(N) linear {\sigma} model, if the auxiliary field is eliminated using the stationary values for the corresponding one- and two-point functions. We numerically compute the chiral condensate and the {\sigma}- and {\pi}-meson masses at nonzero temperature in the one-loop approximation of the CJT formalism. The order of the chiral phase transition depends sensitively on the choice of the renormalization scheme. In the linear version of the model and for explicitly broken chiral symmetry, it turns from crossover to first order as the mass of the {\sigma} particle increases. In the nonlinear case, the order of the phase transition turns out to be of first order. In the region where the parameter space of the model allows for physical solutions, Goldstone's theorem is always fulfilled.