Thermodynamic approach to proton number fluctuations in baryon-rich heavy-ion matter created at moderate collision energies

Abstract

We point out how proton number cumulants measured in heavy-ion collisions within a momentum space acceptance can be related to the grand-canonical cumulants of baryon number, assuming that particles are emitted from a fireball with uniform distribution of temperature and baryochemical potential, superimposed on a hydrodynamic flow velocity profile. Analysis of recent experimental measurements of the HADES Collaboration shows that the rapidity acceptance dependence of proton cumulants is consistent with thermal emission of nucleons from a grand-canonical heat bath. The extracted baryon number susceptibilities exhibit an hierarchy χ1 , indicating large non-Gaussian fluctuations that might point to the presence of the QCD critical point close to the chemical freeze-out of √ sNN = 2.4 GeV Au-Au collisions at T ∼ 70 MeV and µB ∼ 850 − 900 MeV. However, the description of the experimental data at large rapidity acceptances becomes challenging once the effect of exact baryon number conservation is incorporated, suggesting that more theoretical and experimental studies are needed to reach a firm conclusion.1 We neglect the effects of Fermi-Dirac statistics on the momentum distributions in the present work.

Proton number cumulants and correlation functions from hydrodynamics and the QCD phase diagram

“…The strong increase in proton κ 2 /κ 1 at √ s NN = 2.4 GeV warrants a closer look at the HADES data. In [27] these data were analyzed as a function of rapidity cut y cut within the framework of a Siemens-Rasmussen like fireball model, with chemical and kinetic freeze-out parameters based on Refs. [28,29].…”