Quartic cumulant of baryon number in the presence of a QCD critical point

2020/08/10 by Débora Mroczek, D. Mroczek, Angel R. Nava Acuña +9
Mathematics · Physics and Astronomy · #Baryon #Condensed matter physics #Critical line #Critical phenomena #Critical point (mathematics) #High-Energy Particle Collisions Research #Ising model #Kurtosis #Mathematical analysis #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Quartic function #Statistical physics #Statistics #hep-ph #nucl-ex #nucl-th

paper · pdf · doi:10.1103/physrevc.103.034901

published as Phys. Rev. C 103, 034901 (2021) · 10 pages, 4 figures

arxiv created 2020/08/10 · openalex publication_date 2021/03/04 · arxiv updated 2021/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric representation introduced in earlier literature, which maps the universal three-dimensional Ising equation of state onto the QCD phase diagram using several non-universal parameters. We focus on the quartic cumulant of the baryon number, or baryon number susceptibility \ensuremathχ₄^B, which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the leading singular contribution, that \ensuremathχ₄^B and net-proton kurtosis should show a specific nonmonotonic behavior due to the critical point. In particular, when following the freeze-out curve on the phase diagram by decreasing beam energy, the kurtosis is expected to dip, and then peak, when the beam energy scan passes close to the critical point. We study the effects of the nonuniversal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of \ensuremathχ₄^B. We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in \ensuremathχ₄^B on the freeze-out line below the transition temperature. The critical point contribution to the dip appears only for a narrow set of mapping parameters, when subleading singular terms are sufficiently suppressed.

Citations

• Thermal, chemical and spectral equilibration in heavy-ion collisions
• Real-time evolution of non-Gaussian cumulants in the QCD critical regime
• 3+1 dimensional viscous hydrodynamics at high baryon densities
• Non-Gaussian Fluctuations near the QCD Critical Point
• 3D Ising model: the scaling equation of state
• Universality, the QCD critical and tricritical point, and the quark number susceptibility
• A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions
• Chemical equilibration due to heavy Hagedorn states
• Phase diagram of QCD
• Higher order fluctuations and correlations of conserved charges from lattice QCD
• Chiral crossover in QCD at zero and non-zero chemical potentials
• (3+1)-dimensional dissipative relativistic fluid dynamics at non-zero net baryon density
• The role of the local conservation laws in fluctuations of conserved charges