We investigate the time evolution of higher order cumulants of conserved charges in a volume with the diffusion master equation. Applying the result to the diffusion of non-Gaussian fluctuations in the hadronic stage of relativistic heavy ion collisions, we show that the fourth-order cumulant of net-electric charge at LHC energy is suppressed compared with the recently observed second-order cumulant at ALICE, if the higher order cumulants at hadronization are suppressed compared with their values in the hadron phase in equilibrium. The significance of the experimental information on the rapidity window dependence of various cumulants in investigating the history of the dynamical evolution of the hot medium created in relativistic heavy ion collisions is emphasized.
We investigate the effects of secondary (knockout) protons, which constitute about 20% of the observed protons at STAR, on the higher order cumulants of proton and baryon numbers measured by event-by-event analyses in relativistic heavy ion collisions. We argue that the contribution of this background effect on the cumulants is expressed by a simple formula, and that hence their effects can be removed in the experimental analysis. It is discussed that this background effect has non-negligible contribution to recently observed proton number cumulants at STAR, especially the third-order one, and that the removal of this effect is crucial to investigate the thermodynamical properties of the primordial hot medium appropriately.
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