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

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 root s(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(B)(4) >> -chi(B)(3) >> chi(B)(2) >> chi(B)(1). 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 similar to 70 MeV and mu(B) similar to 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. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

A framework is developed to relate proton number cumulants measured in heavy-ion collisions to baryon number susceptibilities. The experimental results suggest that the rapidity acceptance dependence of proton cumulants is consistent with a thermal emission model, and the extracted baryon number susceptibilities exhibit a hierarchical structure. However, considering the effect of baryon number conservation presents challenges in describing the experimental data at large rapidity acceptances.