Partial correlation analysis method in ultra-relativistic heavy-ion collisions

摘要

We argue that statistical data analysis of two-particle longitudinalcorrelations in ultra-relativistic heavy-ion collisions may be efficientlycarried out with the technique of partial covariance. In this method, thespurious event-by-event fluctuations due to imprecise centrality determinationare eliminated via projecting out the component of the covariance influenced bythe centrality fluctuations. We bring up the relationship of the partialcovariance to the conditional covariance. Importantly, in the superpositionapproach, where hadrons are produced independently from a collection ofsources, the framework allows us to impose centrality constraints on the numberof sources rather than hadrons, that way unfolding of the trivial fluctuationsfrom statistical hadronization and focusing better on the initial-statephysics. We show, using simulated data from hydrodynamics followed withstatistical hadronization, that the technique is practical and very simple touse, giving insight into the correlations generated in the initial stage. Wealso discuss the issues related to separation of the short- and long-rangecomponents of the correlation functions, and show that in our example theshort-range component from the resonance decays is largely reduced byconsidering pions of the same sign. We demonstrate the method explicitly on thecases where centrality is determined with a single central control bin, or withtwo peripheral control bins.