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

TL;DR

This paper develops a thermodynamic framework linking proton number fluctuations in heavy-ion collisions to baryon susceptibilities, analyzing experimental data to explore signals of the QCD critical point.

Contribution

It introduces a model connecting proton cumulants to baryon susceptibilities considering thermal emission and flow, and discusses the impact of baryon number conservation on data interpretation.

Findings

Proton cumulants are consistent with thermal emission from a grand-canonical heat bath.

Baryon number susceptibilities exhibit a hierarchy indicating large non-Gaussian fluctuations.

Exact baryon number conservation complicates the interpretation of large rapidity acceptance data.

Abstract

We develop a framework to relate proton number cumulants measured in heavy-ion collisions within a momentum space acceptance to the susceptibilities 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. The rapidity acceptance dependence of proton cumulants measured by the HADES Collaboration in $\sqrt{s_{\rm NN}} = 2.4$ GeV Au-Au appears to be consistent with thermal emission of nucleons from a grand-canonical heat bath, with the extracted baryon number susceptibilities exhibiting an hierarchy $\chi_4^B \gg -\chi_3^B \gg \chi_2^B \gg \chi_1^B$. Naively, this could indicate large non-Gaussian fluctuations that might point to the presence of the QCD critical point close to the chemical freeze-out at $T \sim 70$ MeV and $\mu_B \sim 850-900$ 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.