Connecting fluctuation measurements in heavy-ion collisions with the grand-canonical susceptibilities

Volodymyr Vovchenko,Oleh Savchuk,Roman V Poberezhnyuk,Mark I Gorenstein,Volker Koch

doi:10.1016/j.physletb.2020.135868

Abstract

We derive the relation between cumulants of a conserved charge measured in a subvolume of a thermal system and the corresponding grand-canonical susceptibilities, taking into account exact global conservation of that charge. The derivation is presented for an arbitrary equation of state, with the assumption that the subvolume is sufficiently large to be close to the thermodynamic limit. Our framework – the subensemble acceptance method (SAM) – quantifies the effect of global conservation laws and is an important step toward a direct comparison between cumulants of conserved charges measured in central heavy ion collisions and theoretical calculations of grand-canonical susceptibilities, such as lattice QCD. As an example, we apply our formalism to net-baryon fluctuations at vanishing baryon chemical potentials as encountered in collisions at the LHC and RHIC.

Highlights

Studies of the QCD phase diagram are one of the focal points of current experimental heavy-ion collision programs [1]
In contrast to prior works studying the ideal hadron resonance gas (HRG) model, our subensemble acceptance method works for an arbitrary equation of state, under the assumption that the acceptance is sufficiently large to reach the thermodynamic limit, and to capture all the relevant physics
The formalism is most suitable for central collisions of ultrarelativistic heavy-ion collisions at the highest energies where we have a strong space-momentum correlations, and it enables direct comparisons between experimental data on cumulants of conserved charges and theoretical calculations of grand-canonical susceptibilities within effective QCD theories and lattice QCD simulations

Summary

Introduction

Studies of the QCD phase diagram are one of the focal points of current experimental heavy-ion collision programs [1]. Under consideration, in particular they provide information about the possible phase changes, including remnants of the chiral criticality at vanishing chemical potential [5] They are calculated either using first-principle lattice QCD simulations [6,7], or in various effective QCD approaches [8,9]. In order to capture the physics of e.g. chiral criticality the effect of charge conservation needs to be understood very well, since reducing the acceptance window even further risks eliminating all the non-trivial effects associated with relevant QCD dynamics [15]. In the present letter we generalize the relation (1) between the GCE susceptibilities χnB and measured cumulants of conserved charge κn[B] to make it valid for subsystems that are comparable in size to the total system. Further assuming strong space-momentum correlations, as is the case for LHC and top RHIC energies, the formalism presented here connects the measured cumulants with those obtained in lattice QCD over a wide range of acceptance windows

Formalism

Net baryon fluctuations at LHC and top RHIC energies

Summary