Rapidity window dependences of higher order cumulants and diffusion master equation

TL;DR

This paper develops an analytic framework using the diffusion master equation to study how higher order cumulants of conserved charges depend on rapidity windows in relativistic heavy ion collisions, revealing insights into non-equilibrium fluctuations.

Contribution

It provides the first analytic formulas for the time evolution of higher order cumulants in a rapidity window for arbitrary initial conditions, linking fluctuation properties to medium characteristics.

Findings

Characteristic structures in cumulant dependence reflect non-equilibrium properties.

Higher order cumulants can reveal thermal and transport properties of the hot medium.

Formulas for cumulants of sub-probability distributions are derived.

Abstract

We study the rapidity window dependences of higher order cumulants of conserved charges observed in relativistic heavy ion collisions. The time evolution and the rapidity window dependence of the non-Gaussian fluctuations are described by the diffusion master equation. Analytic formulas for the time evolution of cumulants in a rapidity window are obtained for arbitrary initial conditions. We discuss that the rapidity window dependences of the non-Gaussian cumulants have characteristic structures reflecting the non-equilibrium property of fluctuations, which can be observed in relativistic heavy ion collisions with the present detectors. It is argued that various information on the thermal and transport properties of the hot medium can be revealed experimentally by the study of the rapidity window dependences, especially by the combined use, of the higher order cumulants. Formulas of higher order cumulants for a probability distribution composed of sub-probabilities, which are useful for various studies of non-Gaussian cumulants, are also presented.