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

## TL;DR

This paper introduces a partial covariance analysis method for two-particle correlations in ultra-relativistic heavy-ion collisions, effectively removing centrality fluctuation effects and providing clearer insights into initial-state physics.

## Contribution

The paper presents a novel application of partial covariance to analyze correlations, allowing centrality constraints on sources and reducing trivial fluctuations in heavy-ion collision data.

## Key findings

- Partial covariance effectively removes centrality fluctuation effects.
- The method simplifies analysis of initial-state correlations.
- Short-range correlations from resonance decays are largely reduced.

## Abstract

We argue that statistical data analysis of two-particle longitudinal correlations in ultra-relativistic heavy-ion collisions may be efficiently carried out with the technique of partial covariance. In this method, the spurious event-by-event fluctuations due to imprecise centrality determination are eliminated via projecting out the component of the covariance influenced by the centrality fluctuations. We bring up the relationship of the partial covariance to the conditional covariance. Importantly, in the superposition approach, where hadrons are produced independently from a collection of sources, the framework allows us to impose centrality constraints on the number of sources rather than hadrons, that way unfolding of the trivial fluctuations from statistical hadronization and focusing better on the initial-state physics. We show, using simulated data from hydrodynamics followed with statistical hadronization, that the technique is practical and very simple to use, giving insight into the correlations generated in the initial stage. We also discuss the issues related to separation of the short- and long-range components of the correlation functions, and show that in our example the short-range component from the resonance decays is largely reduced by considering pions of the same sign. We demonstrate the method explicitly on the cases where centrality is determined with a single central control bin, or with two peripheral control bins.