Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions

TL;DR

This paper develops methods to accurately measure and interpret event-by-event fluctuations in net-particle numbers in relativistic nuclear collisions, accounting for non-dynamical effects like impact parameter fluctuations and conservation laws.

Contribution

It introduces a rigorous approach to correct for participant fluctuations and other non-dynamical contributions in fluctuation measurements across different energies and cumulant orders.

Findings

Participant fluctuations vanish at mid-rapidity for LHC energies in second and third cumulants.

Higher even-order cumulants remain non-zero even when net-baryon number is zero.

Corrections for participant fluctuations become significant at lower energies and must be applied for accurate theory comparison.

Abstract

We develop methods to deal with non-dynamical contributions to event-by-event fluctuation measurements of net-particle numbers in relativistic nuclear collisions. These contributions arise from impact parameter fluctuations and from the requirement of overall net-baryon number or net-charge conservation and may mask the dynamical fluctuations of interest, such as those due to critical endpoints in the QCD phase diagram. Within a model of independent particle sources we derive formulae for net-particle fluctuations and develop a rigorous approach to take into account contributions from participant fluctuations in realistic experimental environments and at any cumulant order. Interestingly, contributions from participant fluctuations to the second and third cumulants of net-baryon distributions are found to vanish at mid-rapidity for LHC energies while higher cumulants of even order are non-zero even when the net-baryon number at mid-rapidity is zero. At lower beam energies the effect of participant fluctuations increases and induces spurious higher moments. The necessary corrections become large and need to be carefully taken into account before comparison to theory. We also provide a procedure for selecting the optimal phase-space coverage of particles for fluctuation analyses and discuss quantitatively the necessary correction due to global charge conservation.