Centrality fluctuations and decorrelations in heavy-ion collisions

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 $\langle V_b\rangle_{N_a}$ and $\langle N_b\rangle_{N_a}$ increase linearly with $N_a$ in mid-central collisions, but flatten out in ultra-central collisions. Such non-linear behavior is sensitive to the centrality resolution of $N_a$. In the presence of centrality decorrelations, the scaled variances $\langle(\delta V_b)^2\rangle/\langle V_b\rangle$ and $\langle(\delta N_b)^2\rangle/\langle N_b\rangle$ are found to decrease linearly with $N_a$ in mid-central collisions, while the $p(n)$ leads to another sharp decrease in the ultra-central 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.