Spontaneous CP violation in the strong interaction at θ = π

Spontaneous CP violation in the strong interaction is analyzed at theta = pi within the framework of the two-flavor Nambu-Jona-Lasinio 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.