Partial correlation analysis method in ultrarelativistic heavy-ion collisions

We argue that statistical data analysis of two-particle longitudinal correlations in ultrarelativistic 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.

Figure 1

Two-particle $\overline{C}$ correlation (with removed autocorrelations) in pseudorapidity of hadron multiplicities for the simulated data (a) for all charged particles after resonance decays and (b) for the primordial hadrons. Wounded quark model, 3+1D viscous event-by-event hydrodynamics, statistical hadronization. Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ in centrality class 30–40%.

Figure 2

Partial $C$-correlation function for the source multiplicities with the central reference bin (a) for the BT model and (b) for the simulated data with primordial hadrons.

Figure 3

Partial $C$-correlation function for the source multiplicities for the simulated data for all charged hadrons, obtained with (a) the central reference bin and (b) with the sum of left and right peripheral bins.

Figure 4

Partial $C$-correlation function for the source multiplicities for the simulated data for ${\pi }^{+}$, with (a) the central reference bin and (b) with the sum of left and right peripheral bins.

Figure 5

Partial $\rho$ correlation for the source multiplicities (a) for the BT model and (b) for the simulated data with primordial hadrons.

Figure 6

Partial $C$-correlation function for the source multiplicities with two peripheral reference bins, obtained for the simulated data with (a) primordial hadrons and (b) all positively charged pions, ${\pi }^{+}$.