QCD with Chiral Chemical Potential: Models Versus Lattice

An emergence of local spatial parity breaking (LPB) in central heavy-ion collisions (HIC) at high energies is discussed. The QCD phenomenology of LPB in the fireball is induced by a difference between the number densities of right- and left-handed chiral fermions which is triggered by a chiral (axial) chemical potential. For the description of peculiarities of LPB, a number of QCD-inspired models are considered and confronted to certain lattice results. In particular, from the meson effective Lagrangian, it is found that the lightest states may become massless and some scalars turn out to be stable. In experimental studies, the asymmetry in production of longitudinal and transverse polarized states of ρ and ω mesons for different values of the invariant mass can serve as a characteristic indication of local spatial parity breaking which can be derived from an abnormal yield of dilepton pairs in the PHENIX, STAR and ALICE collaborations.