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; we argue that this is a consequence of the strict boost invariance of the initial field configurations. A substantial generation of topological charge, as required in the P-odd bubble scenario [D. Kharzeev, et al., Phys. Rev. Lett. 81 (1998) 512], can only occur if strict boost invariance is lost in the later stages of the collision. This could be naturally achieved if the system approaches thermalization.