Real time evolution of non-Gaussian cumulants in the QCD critical regime

We derive a coupled set of equations that describe the non-equilibrium evolution of cumulants of critical fluctuations for space-time trajectories on the cross-over side of the QCD phase diagram. In particular, novel expressions are obtained for the non-equilibrium evolution of non-Gaussian Skewness and Kurtosis cumulants. Utilizing a simple model of the space-time evolution of a heavy- ion collision, we demonstrate that, depending on the relaxation rate of critical fluctuations, Skewness and Kurtosis can differ significantly in magnitude as well as in sign from equilibrium expectations. Memory effects are important and shown to persist even for trajectories that skirt the edge of the critical regime. We use phenomenologically motivated parameterizations of freeze-out curves, and of the beam energy dependence of the net baryon chemical potential, to explore the implications of our model study for the critical point search in heavy-ion collisions.