Quantifying fluctuation signatures of the QCD critical point using maximum entropy freeze-out

Abstract

A key question about the QCD phase diagram is whether there is a critical point somewhere on the boundary between the hadronic and quark-gluon plasma phases, and if so where. Heavy-ion collisions offer a unique opportunity to search for signatures of such a critical point by analyzing event-by-event fluctuations in particle multiplicities. To draw meaningful conclusions from experimental data, a theoretical framework is needed to link QCD thermodynamics with the particle spectra and correlations observed in detectors. The Equation of State (EoS) of QCD near a critical point can be related to the universal Gibbs free energy of the 3D Ising model using four currently unknown non-universal mapping parameters whose values are determined by the microscopic details of QCD. We utilize the maximum entropy approach to freeze-out the fluctuations in order to make estimates for factorial cumulants of proton multiplicities, assuming thermal equilibrium, for a family of EoS with a 3D Ising-like critical point, varying the microscopic inputs that determine the strength and structure of the critical features. We quantify the effect of the non-universal mapping parameters, and the distance between the critical point and the freeze-out curve, on the factorial cumulants of proton multiplicities.

Figures (13)

• Figure 1: Contours of the critical magnitude of the squared correlation length scaled by $w^2$, $\xi_{\rm{QCD}}^2/w^2$ in units of $f_\xi$, for several values of the equation of state parameters $w$ and $\rho$. We have placed the critical point at $\mu_c=600$ MeV with a temperature $T_c=90$ MeV chosen so as to put the critical point on the chiral crossover curve estimated from lattice QCD calculations Borsanyi:2020fev. We have chosen the second mapping angle to be given by $\alpha_2=0^{\circ}$. The dotted line shows the Ising $h$-axis, while the dashed line shows the Ising $r$-axis which follows the chiral crossover line by construction.
• Figure 2: Three freezeout curves displaced downward relative to the crossover curve $\Delta T'=0$ (orange) by $\Delta T_f=4$, 6 and 9 MeV (solid blue, red and black curves, respectively). By construction, the Ising-$r$ axis maps onto the crossover curve. Because we have chosen $\alpha_2=0$, the Ising-$h$ axis maps onto the horizontal orange dotted line. The dashed blue, red and black curves are curves of constant Ising-$h$ that are coincident with the three freezeout curves where the freezeout curves each cross the Ising-$h$ axis. We see that the freezeout curves are close to being curves of constant $h$.
• Figure 3: Contours of the critical contribution to $V T^{-3}_c \Delta H_{2n}=V T_c^{-3}\langle\delta n^2\rangle$ plotted for various values of the nonuniversal equation of state mapping parameters $w$ and $\rho$, with $\mu_c=600 \, \text{MeV}$, $T_c=90$ MeV, and $\alpha_2=0^{\circ}$. The dotted line reflects this choice of $\alpha_2=0^{\circ}$ in that it shows the Ising $h$-axis $r=0$, while the dashed line shows the Ising $r$-axis $h=0$ which, by the construction described in Sect. \ref{['Sec:EoS']}, maps onto the crossover curve on the QCD phase diagram.
• Figure 4: Contours of the critical contribution to $V^2 T^{-3}_c \Delta H_{3n}=V^2 T_c^{-3}\left<\delta n^3\right>$ plotted for various values of the nonuniversal mapping parameters $w$ and $\rho$ with $\mu_c=600 \, \text{MeV}$, $T_c=90$ MeV and $\alpha_2=0^{\circ}$. The dotted line reflects this choice of $\alpha_2=0^{\circ}$ in that it shows the Ising $h$-axis, while the dashed line shows the Ising $r$-axis which is chosen to lie along the QCD crossover curve.
• Figure 5: Contours of the critical contribution to $V^3 T^{-3}_c \Delta H_{4n}=V^{3} T_c^{-3}\left<\delta n^4\right>$ plotted for various values of the nonuniversal mapping parameters $w$ and $\rho$ with $\mu_c=600 \, \text{MeV}$, $T_c=90$ MeV and $\alpha_2=0^{\circ}$. The dotted line reflects this choice of $\alpha_2=0^{\circ}$ in that it shows the Ising $h$-axis, while the dashed line shows the Ising $r$-axis which is chosen to lie along the QCD crossover curve.