Spontaneous CP-violation in the strong interaction at theta = pi

TL;DR

This study investigates spontaneous CP-violation at theta = pi in the strong interaction using the two-flavor NJL model, exploring its dependence on instanton effects, quark masses, and thermodynamic conditions, with implications for meson behavior.

Contribution

It demonstrates how the occurrence of spontaneous CP-violation depends on the 't Hooft interaction strength and examines its phase structure across various physical parameters.

Findings

Spontaneous CP-violation depends on instanton interaction strength.

Agreement with Vafa-Witten theorem at nonzero density and temperature.

Unusual meson mass and mixing features in the CP-violating phase.

Abstract

Spontaneous CP-violation in the strong interaction is analyzed at theta = pi within the framework of the two-flavor NJL model. It is found that the occurrence of spontaneous CP-violation at theta = pi 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. When available a comparison to earlier results from chiral perturbation theory is made. From our results we conclude that spontaneous CP-violation in the strong interaction is an inherently low-energy phenomenon. In all cases we find agreement with the Vafa-Witten theorem, also at nonzero density and temperature. Meson masses and mixing in the CP-violating phase display some unusual features as a function of instanton interaction strength. A modification of the condition for charged pion condensation at nonzero isospin chemical potential and a novel phase of charged a_0 mesons are discussed.