Out-of-equilibrium contributions to charm hadrons in a fluid-dynamic approach

Abstract

Building on previous studies that demonstrated the applicability of a fluid-dynamic description of charm quarks in the quark-gluon plasma, the present work extends the framework by computing the out-of-equilibrium contributions to the distribution function of charm hadrons. The analysis includes corrections arising from the initial out-of-equilibrium distribution of charm quarks after a free-streaming phase, as well as from the freeze-out surface within fluid dynamics. These results enable the exact computation of integrated yields and transverse momentum distributions of charm hadrons for different values of the spatial diffusion coefficient, thereby providing the basis for a systematic determination of the charm transport coefficients. In addition, the limits of applicability of the approach are identified by determining the transverse-momentum region in which charm hadrons are described by a well-defined, positive distribution function.

Figures (6)

• Figure 1: Radial diffusion current (left) and charm quark density profile (right) as a function of radius at the formation time $\tau_i$ and at the QGP initial time $\tau_0$ for Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV for the 0--10% centrality class.
• Figure 2: Radial diffusion current (left) and charm quark density profile (right) as a function of the radius for different times, fixing $D_sT = 0.24$. The comparison of a vanishing initial diffusion current case (solid lines) to that of a free-streaming initialization (dashed lines) is shown.
• Figure 3: Left panel: Integrated yield of $\rm D^0$ meson for different values of $D_sT$, considering a gas composed of $\rm D^0$ only. The non-diffusive case (blue markers) is compared to the equilibrium and the out-of-equilibrium contributions (green and red markers, respectively), as well as considering the total distribution function (orange markers). The $\rm D^0$ yield is also compared to the total number of charm quarks (black dashed line). Right panel: Integrated yields of various charm hadrons in the non-diffusive and in the diffusive scenarios, with and without out-of-equilibrium corrections.
• Figure 4: Momentum distribution of $D^0$ mesons for $D_sT = 0.1$ (left) and $D_sT = 0.24$ (right), comparing the non-diffusive case (blue line) with the diffusive scenario, shown for the equilibrium (green line) and total (orange line) distribution functions.
• Figure 5: Left panel: ratio between the out-of-equilibrium and the equilibrium contribution of $\rm D^0$ meson momentum spectrum for different values of $D_sT$. To guide the eye, a black dashed line has been drawn at $-1$. Right panel: Study of the zero-crossing of $p_{\rm T}$ spectra as a function of $D_sT$. At high values of $D_sT$, the value of $p_{\rm T}$-crossing approaches the mass of the corresponding charm hadron (reported as dashed lines), with the exception of $\rm J/\Psi$ meson.