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The amount of axial charge produced in heavy ion collisions is one of the keyquantities in understanding chiral magnetic effect. Current phenomenologicalstudies assume large axial charge chemical potential $\mu_5$ produced in Glasmaphase and assume the conservation of axial charge throughout the evolution,which is valid in the long relaxation time limit. Based on the solution ofstochastic hydrodynamics with phenomenological parameters, our study suggeststhat the situation of heavy ion collisions may be close to the opposite limit,in which axial charge fluctuation approaches thermodynamic limit. Using $\mu_5$set by the thermodynamic limit for chiral magnetic effect and a background fromparity-even $v_1$, we obtain a reasonable description of the centralitydependence of charged particle correlation measured in experiment.

Axial Charge Fluctuation and Chiral Magnetic Effect from Stochastic Hydrodynamics