  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.
