Spontaneous CP violation in the NJL model at theta = pi

TL;DR

This paper investigates spontaneous CP violation at theta = pi within the two-flavor NJL model, analyzing how various parameters influence the phase structure and CP-violating phenomena, including modifications to pion condensed phases.

Contribution

It demonstrates the dependence of spontaneous CP violation on the 't Hooft interaction strength and explores its behavior under different physical conditions in the NJL model.

Findings

CP violation depends on 't Hooft interaction strength

Phase structure varies with quark masses, temperature, and chemical potentials

Modification of charged pion condensed phase observed

Abstract

As is well-known, spontaneous CP-violation in the strong interaction is possible at theta = pi, which is commonly referred to as Dashen's phenomenon. This phenomenon has been studied extensively using chiral Lagrangians. Here the two-flavor NJL model at theta = pi is discussed. It turns out that the occurrence of spontaneous CP-violation depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. The latter dependence shows a modification of the charged pion condensed phase first discussed by Son and Stephanov.