Centrality fluctuations and decorrelations in heavy-ion collisions in a Glauber model

The centrality or the number of initial-state sources V of the system produced in heavy ion collision is a concept that is not uniquely defined and subject to significant theoretical and experimental uncertainties. We argue that a more robust connection between the initial-state sources with final-state multiplicity could be established from the event-by-event multiplicity correlation between two subevents separated in pseudorapidity, Na vs Nb. This correlation is sensitive to two main types of centrality fluctuations (CF): (1) particle production for each source p(n) which smears the relation between V and Na used for experimental centrality and (2) decorrelations between the sources in the two subevents Vb and Va. The CF is analyzed in terms of cumulants of Vb and Nb as a function of Na, i.e., experimental centrality is defined with Na. We found that the mean values VbNa and NbNa increase linearly with Na in midcentral collisions but flatten out in ultracentral collisions. Such nonlinear behavior is sensitive to the centrality resolution of Na. In the presence of centrality decorrelations, the scaled variances ((δVb)2)/Vb and ((δNb)2)/Nb are found to decrease linearly with Na in midcentral collisions, while the p(n) leads to another sharp decrease in the ultracentral region. The higher-order cumulants of Vb and Nb show interesting but rather complex behaviors which deserve further studies. Our results suggest that one can use the cumulants of the two-dimensional multiplicity correlation, especially the mean and variance, to constrain the particle production mechanism as well as the longitudinal fluctuations of the initial-state sources.