Anomalous chirality fluctuations in the initial stage of heavy ion collisions and parity odd bubbles

We compute numerically the topological charge distribution in the initial stage of a high energy heavy ion collision. This charge distribution is generated by Chern-Simons number fluctuations associated with the dynamics of strong classical fields in the initial state. The distribution is found to be quite narrow at RHIC and LHC energies reflecting a small value of the topological susceptibility. Thus the effective potential of classical fields is shallow in the $\theta$-direction likely creating favorable conditions for the subsequent generation of P-odd bubbles.