The chiral imbalance (ChI) is given by a difference between the numbers of RH and LH quarks which may occur in the fireball after heavy ion collision. To characterize it adiabatically a quark chiral (axial) chemical potential must be introduced taking into account emergence of a ChI in such a phase. In this report the phenomenology of formation of Local spatial Parity Breaking (LPB) in the hot and dense baryon matter is discussed and its simulation within a number of QCD-inspired models is

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... ned. The appearance of new states in the spectra of scalar, pseudoscalar and vector particles in such a matter is elucidated. In particular, from the effective vector meson theory in the presence of Chern-Simons interaction it is demonstrated that the spectrum of massive vector mesons splits into three polarization components with different effective masses. The asymmetry in production of longitudinally and transversely polarized states of ρ and ω mesons for various values of the dilepton invariant mass can serve as a characteristic indication of the LPB in PHENIX, STAR and ALICE experiments. Introduction: Chiral Imbalance in Heavy Ions Collisions The behaviour of baryonic matter under extreme conditions in HIC has received a lot of attention [1, 2] . New properties of QCD in the environment were tested in current accelerator experiments on RHIC and LHC [3] . A medium generated in these collisions (a fireball) may serve for experimental and theoretical studies of various phases of a matter. The dedicated experimental study of hadron correlations in non-central heavy-ion collisions at RHIC [4] and LHC [5] revealed a signal of the separation of electric charges predicted in [6] as a signature of local P-and CP-odd fluctuations in QCD matter. The subsequent studies [7, 8] improved the theoretical understanding of the underlying phenomenon, the "chiral magnetic effect" (CME) in the reactions for peripheral ion collisions (see [9] for a review) . On the contrary, a gradient density of isosinglet pseudoscalar condensate can be formed as a result of large, "long-lived" topological fluctuations of gluon fields in the fireball in central collisions (see [10] for details). To describe various effects of hadron matter in a fireball with parity breaking, we must introduce the axial/ chiral chemical potential [10] . At finite temperature, the transitions between