Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point

TL;DR

This paper investigates how higher moments of particle multiplicity fluctuations in heavy ion collisions can signal the QCD critical point, proposing parameter-independent ratios of observables for its detection and characterization.

Contribution

It provides quantitative estimates of critical fluctuation contributions to higher moments and introduces ratios of observables that are independent of non-universal parameters for identifying the critical point.

Findings

Critical fluctuations significantly enhance higher moments of multiplicity distributions.

Parameter-independent ratios can reliably signal the proximity to the QCD critical point.

Ratios can also constrain non-universal parameters if the critical point is located.

Abstract

The QCD critical point can be found in heavy ion collision experiments via the non-monotonic behavior of many fluctuation observables as a function of the collision energy. The event-by-event fluctuations of various particle multiplicities are enhanced in those collisions that freeze out near the critical point. Higher, non-Gaussian, moments of the event-by-event distributions of such observables are particularly sensitive to critical fluctuations, since their magnitude depends on the critical correlation length to a high power. We present quantitative estimates of the contribution of critical fluctuations to the third and fourth moments of the pion, proton and net proton multiplicities, as well as estimates of various measures of pion-proton correlations, all as a function of the same five non-universal parameters, one of which is the correlation length that parametrizes proximity to the critical point. We show how to use nontrivial but parameter independent ratios among these more than a dozen fluctuation observables to discover the critical point. We also construct ratios that, if the critical point is found, can be used to overconstrain the values of the non-universal parameters.