Vector mesons spectrum in a medium with a chiral imbalance induced by the vacuum of fermions

The properties of the light vector mesons in the presence of local parity breaking medium with a chiral imbalance are considered in the vector-meson dominance model. Applying the finite lowest-order radiatively induced local effective Lagrangian, initially developed for the QED, for the vector $\rho$ and $\omega$ mesons, we obtained the mass spectrum as a function of momentum and chiral chemical potential $\mu_5$. We showed that in addition to the Chern-Simons term, splitting the transverse polarisations of the mesons, there is another radiatively induced contribution that becomes important at momentum and $\mu_5$ around a few hundred MeV.