Spontaneous violation of spatial parity in dense baryonic matter in a generalized $U(2)_{\mathrm L}{\times}U(2)_{\mathrm R}$ sigma model

Based on a generalized $U(2)_{\mathrm L}{\times}U(2)_{\mathrm R}$ sigma model describing ground and excited states of scalar and pseudoscalar meson singlets and triplets, we investigate the conditions for spatial parity violation for dense baryonic matter in the hadron phase. We introduce `t Hooft-type vertices into the model for violating the $U(1)_{\mathrm A}$ symmetry of quantum chromodynamics by the anomaly. At large values of the chemical potential, broken-parity states can appear in the model, which corresponds to condensation of pseudoscalar fields. We give the conditions on the parameters of the generalized sigma model that determine the transition to the phase with spontaneously broken parity. For different signs of the constants of two `t Hooft-type vertices, either pseudoscalar isotriplets or isosinglets undergo condensation.