In the context of the search for the QCD critical point using
non-Gaussian fluctuations, we obtain the evolution equations for
non-Gaussian cumulants within hydrodynamics to leading order of the
systematic expansion in the magnitude of thermal fluctuations. We
develop diagrammatic technique in which the leading order
contributions are given by tree diagrams. We introduce the concept of
Wigner transform for multipoint correlators and derive the evolution
equations for the novel three- and four-point Wigner functions. We
demonstrate in a simple model simulation how this formalism accounts
for the effects of memory and baryon number conservation on critical
point signatures in non-Gaussian fluctuations.
References: Phys.Rev.Lett. 127 (2021) 7, 072301 and work in progress.