Particle Spectra in the Integrated HydroKinetic Model at RHIC BES Energies

TL;DR

The paper tackles how to reproduce light-hadron transverse momentum spectra in Au+Au collisions at RHIC BES energies using an extended iHKM (iHKMe) that unifies pre-equilibrium dynamics, hydrodynamics, and hadronic transport. It tests two equations of state—a crossover (CO) and a first-order phase transition (PT)—while treating thermalization as a tunable rate and exploring the impact of the hydrodynamic-to-transport switching energy density $\epsilon_{sw}$. A key finding is that the total thermalization duration is about $1\ \mathrm{fm}/c$ across $7.7\le\sqrt{s_{NN}}\le 39$ GeV, with the onset occurring near or slightly before full overlap, $\tau_0\approx 0.75\tau_{\text{overlap}}$, and that after parameter tuning both EoS describe the soft spectra comparably, though notable differences appear at $\sqrt{s_{NN}}=7.7$ GeV in proton and kaon yields due to trajectories in the $T$–$\mu_B$ plane and the choice of $\epsilon_{sw}$. The work highlights the importance of pre-equilibrium dynamics and switching conditions and lays groundwork for future studies of additional bulk observables such as elliptic flow.

Abstract

We study light-hadron production in Au+Au collisions at $\sqrt{s_{NN}} = 7.7-39$ GeV using an extended Integrated HydroKinetic Model (iHKMe). Focusing on transverse momentum spectra, we investigate the sensitivity to key model parameters, in particular the thermalization time scale. We consider two distinct equations of state: one featuring a crossover and the other a first-order phase transition. In both cases, thermalization begins shortly before full nuclear overlap and lasts approximately 1~fm/$c$ across all energies. Both equations of state provide a similarly good description of the soft particle momentum spectra once the other parameters are slightly adjusted. The most pronounced differences arise at the lower RHIC BES energy of $\sqrt{s_{NN}} = 7.7$ GeV, particularly in proton and kaon yields, reflecting their sensitivity to the freeze-out parameters.

Figures (5)

• Figure 1: Transverse momentum ($p_T$) spectra for $\pi^-$, $p$, and $\bar{p}$ (from left to right) averaged over $750$ simulations, with one standard deviation from the mean values, using sets with random parameters within the ranges presented in Table \ref{['tab:latinCube']}. Data correspond to Au+Au collisions at $\sqrt{s_{NN}}=14.5$ GeV and 20-30% centrality class.
• Figure 2: Correlation coefficients between the five model parameters and the transverse momentum spectra at low, intermediate, and high $p_{\text{T}}$ for $\pi^-$, $p$, and $\bar{p}$ in $20-30\%$ centrality Au+Au collisions at $\sqrt{s_{NN}}=14.5$ GeV. The results for $\pi^{-}$ mesons and protons (shown in the two tables on the left) are very similar for both equations of state; therefore, only the crossover case is shown. For kaons, the correlation matrices are similar to those of pions. For antiprotons (shown in the two plots on the right), we present the results for both scenarios.
• Figure 3: Inferred $\tau_0$ values vs nuclei overlapping time from Eq. (\ref{['eq:overlapTime']}) with $0.75$ factor. The grey shaded zone reflects the estimated uncertainty of $\tau_0$ for the crossover equation of state.
• Figure 4: Comparison of iHKM results with STAR dataSTAR:2017salSTAR:2019vcp for $\pi^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ in the 20–30% centrality class at midrapidity ($|y| < 0.1$). The pion spectra were used to calibrate the $\tau_0$ and $\tau_{\text{th}}$ parameters.
• Figure 5: Comparison of iHKM results with STAR data STAR:2017salSTAR:2019vcp for $\pi^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ in the 0–5% centrality class at midrapidity ($|y| < 0.1$).