Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions

Abstract

We explore the relation between proton and nucleon number fluctuations in the final state in relativistic heavy ion collisions. It is shown that the correlations between the isospins of nucleons in the final state are almost negligible over a wide range of collision energy. This leads to a factorization of the distribution function of the proton, neutron, and their antiparticles in the final state with binomial distribution functions. Using the factorization, we derive formulas to determine nucleon number cumulants, which are not direct experimental observables, from proton number fluctuations, which are experimentally observable in event-by-event analyses. With a simple treatment for strange baryons, the nucleon number cumulants are further promoted to the baryon number ones. Experimental determination of the baryon number cumulants makes it possible to compare various theoretical studies on them directly with experiments. Effects of nonzero isospin density on this formula are addressed quantitatively. It is shown that the effects are well suppressed over a wide energy range.

Mapping the phases of quantum chromodynamics with beam energy scan

“…That is, the initial proton can be stopped either as a proton or a neutron with equal probability, see Refs. [328,329].…”

Energy Dependence of Moments of Net-Proton Multiplicity Distributions at RHIC

“…The measurements presented here are within a finite acceptance range and use only the protons among the produced baryons. References [19,20] discuss the advantages of using net-baryon measurements and effects of acceptance.…”

Off-diagonal cumulants of net-charge, net-proton and net-kaon multiplicity distributions in Au+Au collisions at √sNN=7.7-200 GeV from STAR

“…The cumulants and their ratios were calculated as a function of the reference multiplicity and then averaged over the centrality bins to suppress the volume fluctuations over wide centrality bins [17,18]. We use embedding Monte Carlo simulation techniques to obtain the efficiencies and an algebra based on binomial detector response to efficiency correction [19,20,21]. The statistical uncertainty estimation is based on the numerical error propagation method of multivariate cumulants [22].…”