Analysis of dilepton angular distributions in a parity breaking medium

We investigate how local parity breaking (LPB) due to large topological fluctuations may affect hadron physics. A distorted dispersion relation is derived for the lightest vector mesons $\rho$ and $\omega$. They are characterised by a mass splitting depending on their polarization. We present a detailed analysis of the angular distribution associated to the lepton pairs created from these mesons searching for polarization dependencies. Two angular variables are found to carry the main information related to the parity breaking effect. Possible signatures for experimental detection of local parity breaking that could potentially be seen by the PHENIX and STAR collaborations are discussed.