Equation of state and cumulants of proton multiplicity in equilibrium near critical point from Pade estimates

Abstract

The fluctuations of proton multiplicity in heavy-ion collisions are the key observables in the search for the QCD critical point. In this work we present an approach to constraining the cumulants of proton number based on the analytical properties of the QCD equation of state in the vicinity of the critical point. We show that, under the assumption of local equilibrium, the features of the collision energy dependence, such as the peaks and the dips of the cumulants, are significantly constrained by the data on the Lee-Yang singularity structure available via Pade resummation of the lattice QCD data. Furthermore, we identify four topologically distinct scenarios, all within the uncertainty range of the Pade estimates for the non-universal mapping parameters, classified based on the location of the critical point and the slope of the chiral crossover curve with respect to the freeze-out curve. These different scenarios result in qualitatively different critical signatures, especially for the third factorial cumulant and thus could be potentially discriminated using the experimental data.

Figures (13)

• Figure 1: Estimated widths of confinement and chiral transitions from the lattice borsanyi2024qcddeconfinementtransitionline. The two estimates based on Padé resummation for the critical point are shown in red and blue. The black dots indicate the three exemplary locations for the critical point we choose (see Table \ref{['table:parameters-Pade']}).
• Figure 2: The constraint on $\bar{\rho}(\alpha_2)$ for the temperatures we use in the critical point scenarios. The band stems from the uncertainty in $c_2$ given in Table \ref{['table:Pade']}.
• Figure 3: A parameterization of the experimental freeze-out curve given in Ref. Andronic:2017pug overlaid with different freeze-out data points.
• Figure 4: An example of scenario H (hot critical point without crossing). $\Delta H_{2n}, \, \Delta H_{3n},\, \Delta H_{4n}$ for $\mu_c = 610\,\text{MeV}$, $T_c = 103\,\text{MeV}$, $\alpha_1 = 13^{\circ}$, $\bar{\rho}=\bar{\rho}_{\text{max}}$, and $w = 5$. Top row: $\alpha_2=5^{\circ}$, bottom row: $\alpha_2=-89^{\circ}$. The dashed black, the dotted black and the white curves represent the $r$ axis (the cross-over curve), the $h$ axis and the freeze-out curve respectively.
• Figure 5: An example of scenario HX (hot critical point with crossing). $\Delta H_{2n}, \, \Delta H_{3n},\, \Delta H_{4n}$ for $\mu_c = 610\,\text{MeV}$, $T_c = 103\,\text{MeV}$, $\alpha_1 = 10^{\circ}$, $\bar{\rho}=\bar{\rho}_{\text{max}}$, and $w = 5$. Top row: $\alpha_2=5^{\circ}$, bottom row: $\alpha_2=-89^{\circ}$. The dashed, dotted and thick lines are the same as in Fig. (\ref{['Fig:HydroHotWithoutCrossing']}).