Evolution and fluctuations of chiral chemical potential in heavy ion collisions

The possible appearance of the effects of local parity breaking in the QCD medium formed in heavy ion collisions due to violation of chiral symmetry can be quantified by corresponding chiral chemical potential $\mu_5$. The experimental observables sensitive to the effects of local parity violation in strong interaction include search for polarisation splitting of the $\rho_0$ and $\omega_0$ mesons via angular dependence of spectral functions in their decay to leptons. In this paper we study the space-time evolution and fluctuations of $\mu_5$ using relativistic hydrodynamics and estimate their effect on the light vector meson polarization splitting in Pb-Pb collisions at LHC energy.