Hydrodynamics of charge fluctuations and balance functions

We apply stochastic hydrodynamics to the study of charge density fluctuations in QCD matter undergoing Bjorken expansion. We find that the charge density correlations are given by a time integral over the history of the system, with the dominant contribution coming from the QCD crossover region where the change of susceptibility per entropy, chi T/s, is most significant. We study the rapidity and azimuthal angle dependence of the resulting charge balance function using a simple analytic model of heavy-ion collision evolution. Our results are in agreement with experimental measurements, indicating that hydrodynamic fluctuations contribute significantly to the measured charge correlations in high energy heavy-ion collisions. The sensitivity of the balance function to the value of the charge diffusion coefficient D allows us to estimate the typical value of this coefficient in the crossover region to be rather small, of the order of 1/(2pi T), characteristic of a strongly coupled plasma.