Two-particle multiplicity and momentum correlations in relativistic nuclear collisions

We introduce a two-particle correlation observable that measures multiplicity-momentum correlations and may facilitate an estimate of the level of equilibration of the medium created in relativistic nuclear collisions. We also discuss a mathematical connection between multiplicity-momentum correlations and three other two-particle momentum density and number density correlators. We calculate that multiplicity-momentum correlations should vanish in equilibrium in the Grand Canonical Ensemble, therefore non-zero measured values may indicate that the system has not reached local thermal equilibrium. Information about the level of equilibration of the system is important because many state-of-the-art models assume local equilibration either directly or through the use of an equation of state that makes this assumption. We make estimates of multiplicity-momentum correlations using PYTHIA/Angantyr and find positive values comparable in magnitude to well-measured correlations of transverse momentum fluctuations. We then outline a formalism that can use multiplicity-momentum correlations and correlations of transverse momentum fluctuations to quantify the level of partial thermalization of the system.