On the symmetry improved CJT formalism in the $O(4)$ linear sigma model

TL;DR

This paper applies the symmetry improved CJT formalism to the $O(4)$ linear sigma model, confirming second-order phase transition restoration and Goldstone theorem validity, and compares its effectiveness with large-$N$ methods.

Contribution

It demonstrates the effectiveness of the symmetry improved CJT formalism in analyzing phase transitions in the $O(4)$ model, ensuring Goldstone theorem compliance.

Findings

Confirmed second-order phase transition restoration.

Validated Goldstone theorem in Hartree approximation.

Compared advantages with large-$N$ approximation.

Abstract

By using the symmetry improved CJT effective formalism developed by Pilaftsis and Teresi, the chiral phase transition is reconsidered in the framework of the $O(4)$ linear sigma model in chiral limit. Our results confirm the restorations of the second-order phase transition and the Goldstone theorem in the Hartree approximation. Finally, we explicitly calculate the effective potentials via the order parameter for various temperatures and address advantages of the present method in comparison with the $O(N)$ model in large-$N$ approximation.