Violations of parity and charge conjugation in the theta vacuum with imaginary chemical potential

TL;DR

This paper investigates the spontaneous breaking and restoration of charge conjugation and parity symmetries in the theta vacuum with imaginary chemical potential using the PNJL model, revealing complex symmetry behaviors across temperature changes.

Contribution

It provides a detailed analysis of C and P symmetry behaviors at theta = pi and mu/(iT) = pi, highlighting their spontaneous breaking and restoration patterns with temperature.

Findings

P symmetry is spontaneously broken at zero temperature.

C symmetry is conserved at zero temperature.

P symmetry is restored at higher temperatures after C symmetry is broken.

Abstract

Charge conjugation (C) and Parity (P) are exact symmetries at theta =pi and Theta = mu/(iT)=pi, where theta is the parameter of the so-called theta-vacuum, mu is the imaginary quark-number chemical potential and T is the temperature. Spontaneous breakings of these discrete symmetries are investigated by the the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. At zero T, P symmetry is spontaneously broken while C symmetry is conserved. As T increases, P symmetry is restored just after C symmetry is spontaneously broken, so that either P or C symmetry or both the symmetries are spontaneously broken for any T. The chiral-symmetry restoration and the deconfinement transition at theta =Theta =0 are remnants of the P restoration and the C breaking at theta =Theta =pi, respectively.