Complementary Two-Particle Correlation Observables for Relativistic Nuclear Collisions

TL;DR

This paper derives a mathematical framework linking various two-particle correlation observables in relativistic nuclear collisions, introducing a new multiplicity-momentum correlation and providing tools for validation, interpretation, and model testing.

Contribution

It introduces a unified mathematical relationship among multiple correlation observables, including a novel multiplicity-momentum correlation, for better analysis of nuclear collision data.

Findings

Derived a mathematical relation linking number and momentum density correlations.

Compared model predictions with PYTHIA simulations for all observables.

Proposed a validation and interpretation framework for correlation measurements.

Abstract

Two-particle correlations are a widely used tool for studying relativistic nuclear collisions. Multiplicity fluctuations comparing charge and particle species have been studied as a possible signal for Quark-Gluon Plasma (QGP) and the QCD critical point. These fluctuation studies all make use of particle variances which can be shown to originate with a two-particle correlation function. Momentum correlations and covariances of momentum fluctuations, which arise from the same correlation function, have also been used to extract properties of the nuclear collision medium such as the shear viscosity to entropy density ratio, the shear relaxation time, and temperature fluctuations. Searches for critical fluctuations are also done with these correlation observables. We derive a mathematical relationship between several number and momentum density correlation observables and outline the different physics mechanisms often ascribed to each. This set of observables also contains a new multiplicity-momentum correlation. Our mathematical relation can be used as a validation tool for measurements, as a method for interpreting the relative contributions of different physics mechanisms on correlation observables, and as a test for theoretical and phenomenological models to simultaneously explain all observables. We compare an independent source model to simulated events from PYTHIA for all observables in the set.