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

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 3D 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~${\chi }_4^B$, which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the {\em leading} singular contribution, that ${\chi }_4^B$ and net-proton kurtosis should show a specific non-monotonic 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 non-universal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of~${\chi }_4^B$. We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in ${\chi }_4^B$ on the freezeout line {\em 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.

10 pages, 4 figures

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• Theoretical and Experimental Constraints for the Equation of State of Dense and Hot Matter
• Proton number cumulants and correlation functions in Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7-200$ GeV from hydrodynamics
• Lattice simulations of the QCD chiral transition at real baryon density
• Baryon transport and the QCD critical point
• Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out-of-equilibrium
• Ripples of the QCD Critical Point
• Mapping out the thermodynamic stability of a QCD equation of state with a critical point using active learning
• Holographic approach of the spinodal instability to criticality
• Continuum extrapolated high order baryon fluctuations
• Collision energy dependence of the critical end point from baryon number fluctuations in the Linear Sigma Model with quarks
• Machine learning phase transitions of the three-dimensional Ising universality class
• Pileup Correction on Higher-order Cumulants with Unfolding Approach
• Hydrodynamic description of the baryon-charged quark-gluon plasma
• Non-equilibrium cumulants within model A from crossover to first-order phase transition side
• The effects of the QCD critical point on the spectra and flow coefficients of hadrons
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• Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density
• Off-of-equilibrium effects on Kurtosis Along Strangeness-Neutral Trajectories
• Generalized susceptibilities of net-baryon number based on the 3-dimensional Ising universality class
• Dynamic density correlations in a baryon rich fluid using Mori-Zwanzig-Nakjima projection operator method
• Fixed point behavior of cumulants in the three-dimensional Ising universality class