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, N-a vs N-b. 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 N-a used for experimental centrality and (2) decorrelations between the sources in the two subevents V-b and V-a. The CF is analyzed in terms of cumulants of V-b and N-b as a function of N-a, i.e., experimental centrality is defined with N-a. We found that the mean values < V-b >(Na) and < N-b >(Na) increase linearly with N-a in midcentral collisions but flatten out in ultracentral collisions. Such nonlinear behavior is sensitive to the centrality resolution of N-a. In the presence of centrality decorrelations, the scaled variances <(delta V-b)(2)>/< V-b > and <(delta N-b)(2)>/< N-b > are found to decrease linearly with N-a in midcentral collisions, while the p(n) leads to another sharp decrease in the ultracentral region. The higher-order cumulants of V-b and N-b 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.