Multiparticle long-range rapidity correlations from fluctuation of the fireball longitudinal shape

Abstract

We calculate the genuine long-range multiparticle rapidity correlation functions, C n (y 1 , . . . ,y n ) for n = 2,3,4,5,6, originating from fluctuations of the fireball longitudinal shape. In these correlation functions any contribution from the short-range two-particle correlations, and in general up to particle (n − 1) in C n , is suppressed. The information about the fluctuating fireball shape in rapidity is encoded in the cumulants of coefficients of the orthogonal polynomial expansion of particle distributions in rapidity.

Correlation functions of net-proton multiplicity distributions in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider from a multiphase transport model

“…(13) at √ s N N =7. 7,11.5,19.6,27,39,62.4 and 200GeV. From the figure, we observe that the overall trends of correlation functions for protons and netprotons behave similarly with centrality.…”

“…The ultrarelativistic quantum molecular dynamics (UrQMD) model cannot explain the observed behaviors of the proton correlation functions from STAR [26]. The correlation functions could also be effectively used to study the long-range correlations of the system [27] and describe the asymmetric component of rapidity correlations measured by the ATLAS experiment [28,29].…”

Mapping the phases of quantum chromodynamics with beam energy scan

“…Analogously, for three particles we have [363] (see also, e.g., Ref. [364]) ρ 3 (y 1 , y 2 , y 3 ) = ρ(y 1 )ρ(y 2 )ρ(y 3 ) + ρ(y 1 )C 2 (y 2 , y 3 ) + ρ(y 2 )C 2 (y 3 , y 1 ) +ρ(y 3 )C 2 (y 1 , y 2 ) + C 3 (y 1 , y 2 , y 3 ), (A. 14) where C 3 (y 1 , y 2 , y 3 ) is the three-particle genuine correlation function in rapidity.…”

Cumulants vs correlation functions and the QCD phase diagram at low energies

“…Given Eqs. (13) and (15) this does not imply a priori the presence of any four particle correlations, since for sufficiently large two-particle correlations, C 2 N , the cumulant ratio may be as large as K 4 /K 2 7 without any three-and four-particle correlations.…”

“…The correlation functions Cn are often referred to as "factorial cumulants"[12] 2. See, e.g., Ref [13]. for explicit definitions of higher order correlation functions.…”