Charm Quark Kinetics in Heavy Ion Collisions

TL;DR

The paper investigates charm quark kinetics in hot QCD matter using a quasiparticle model in which temperature-dependent masses and a lattice-QCD–driven running coupling $G(T)$ describe the medium for $N_f=2+1(+1)$ flavors. It compares charm as fixed-mass impurities ($N_f=2+1$) with dynamical charm quasiparticles ($N_f=2+1+1$) under two expansion scenarios: a 1D Bjorken flow and a (2+1)D viscous hydrodynamic expansion, supplying temperature and volume profiles to the charm rate equation. The charm production rate $R_{car{c}}$ is found to be systematically suppressed in the $N_f=2+1+1$ case due to heavier effective masses, and the annihilation channel is subdominant, making production the dominant mechanism near $T_c$. Solving the rate equation with an SHM-derived initial charm yield shows that the total charm number $N_{car{c}}( au)$ remains approximately conserved across all descriptions, with the $N_f=2+1+1$ description yielding final yields most consistent with SHM expectations. These results support the view that charm quark production in the QGP is limited and that the total open charm content is largely determined by initial production rather than in-medium chemical equilibration.

Abstract

We study the evolution of charm $(c)$ quarks in hot QCD matter with $N_f=2+1(+1)$ quark flavors by analyzing the charm production rate and the time dependence of their abundance. Microscopically, the system is described within a quasiparticle model, in which interactions among dynamical quarks and gluons are encoded in their effective masses with the running coupling constrained by lattice QCD data. We investigate $c$-quark kinetics in a longitudinally propagating perfect fluid as well as in a viscous medium undergoing (2+1)D expansion, and find that the charm production rate decreases monotonically across all medium formulations. In the $N_f=2+1+1$ scenario, charm production is systematically suppressed due to the effective mass of heavy quasiparticles. Assuming an initial charm yield given by the Statistical Hadronization Model, we solve the rate equation and compute the total charm abundance in hot QCD medium. For all descriptions considered, the charm quark number remains approximately conserved, consistent with existing experimental evidence.

Figures (6)

• Figure 1: Left: Effective running coupling $G(T)$ as a function of temperature $T$ for hot QCD matter with $N_f=2+1$ (squares) and $N_f=2+1+1$ (circles). The shaded bands indicate the uncertainties propagated form the underlying lQCD data Borsanyi:2013biaBorsanyi:2016ksw. Analytical fits to the corresponding data points are shown by solid lines. Right: Dynamically generated quasiparticle masses $m_i(T)$ as functions of temperature for $N_f=2+1$ (filled symbols) and $N_f=2+1+1$ (open symbols with shaded bands). Gluons $(g)$ are shown by diamonds, charm quarks ($c$) by circles, strange quarks ($s$) by triangles, and light quarks $(l)$ by squares. The dashed line indicates the value of the bare charm quark mass, $M_c=1.3$ GeV.
• Figure 2: Temperature $T$ as a function of proper time $\tau$ for $\textbf{(a)}$ a longitudinally propagating perfect fluid (solid line) and $\textbf{(b)}$ a viscous medium expanding in (2+1) dimensions (squares). Both scenarios start from identical initial conditions, $T_0=0.624$ GeV and $\tau_0=0.2$ fm. The dashed line indicates the pseudocritical temperature, $T_{\rm c}=155$ MeV.
• Figure 3: Volume of the hot QCD medium as a function of a proper time, $V(\tau)$, for different expansion scenarios: $\textbf{(a)}$ purely longitudinal propagation of a perfect fluid (solid line), $\textbf{(b)}$ expansion of a viscous medium in (2+1) dimensions (squares). Both evolutions start at $\tau_0=0.2$ fm with an initial volume per unit rapidity $V_0\simeq 30.8\ \text{fm}^3$, determined from Eqs. \ref{['eq:V']}--\ref{['eq:R_tau']}. The shaded band corresponds to the volume of the fireball per unit rapidity at chemical freezeout, $V_{\rm fin}=4997\pm455\ \text{fm}^3$, used in the SHM Andronic:2021erx (see main text for details). The vertical lines indicate the times at which the QGP reaches the pseudocritical temperature, $T_{\rm c}=155$ MeV: solid line for scenario $\textbf{(a)}$ and dashed line for $\textbf{(b)}$.
• Figure 4: Total cross sections for gluon fusion, $gg\to c\bar{c}$ (left), and light quark-antiquark annihilation, $l\bar{l}\to c\bar{c}$ (right), as functions of the collision energy $\sqrt{s}$ at $T_{\rm c}=155$ MeV for $N_f=2+1$. The QPM results are shown for $M_c=1.3$ GeV (open symbols) and for $M_c=1.5$ GeV (dashed lines), as well as for the case when the cross section is multiplied by a factor of 2 (dotted lines). Alongside, the corresponding DQPM results Song:2024hvv are presented by solid lines. All results correspond to a thermalized QGP with $N_f=2+1$ quark flavors.
• Figure 5: Total charm quark production rate as a function of proper time, $R_{c\bar{c}}(\tau)$. Results are shown for $N_f=2+1$, where $c$ quarks are treated a heavy impurities with constant mass (circles), and for $N_f=2+1+1$ with thermalized charm quasiquarks (squares). The vertical lines indicate the times at which the QGP reaches the pseudocritical temperature, $T_{\rm c}=155$ MeV, for scenario $\textbf{(a)}$ (perfect Bjorken flow, solid line) and $\textbf{(b)}$ (viscous medium expanding in (2+1)D, dashed line).