Broadening of the chiral critical region in a hydrodynamically expanding medium

We investigate higher cumulants of the sigma field as the chiral order parameter at the QCD phase transition. We derive a thermodynamic expression for the skewness and kurtosis from susceptibilities and use these to determine $ S\sigma$ and $ \kappa\sigma^2$ for the sigma field in equilibrium. In a next step, we study the behavior of these cumulants in both an equilibrated static medium and an expanding medium resembling the hydrodynamic stage of a heavy-ion collision. For the latter one, we find a significant broadening of the critical region