Thermalization of Heavy Quarks in the Quark-Gluon Plasma

TL;DR

This work tackles how heavy quarks thermalize in the Quark-Gluon Plasma by augmenting a Fokker-Planck transport framework with resonant heavy-light (D- and B-meson–like) states that can exist above the QCD transition. It builds an effective Lagrangian respecting chiral and heavy-quark symmetry, derives in-medium self-energies and scattering amplitudes for heavy-light processes, and computes drag and diffusion coefficients to feed into a time-dependent FP equation for evolving heavy-quark spectra in an expanding fireball. The main finding is that resonant interactions can enhance the transport coefficients by about a factor of three over perturbative QCD alone, drastically reducing charm-quark equilibration times to a few fm/$c$ at moderate temperatures, and reshaping $p_T$ spectra toward a thermal-like distribution with $T\sim 290$ MeV by the end of the QGP/mixed phase. This has important implications for open-charm observables and the development of elliptic flow, and it motivates further work to refine momentum-dependent transport, include transverse flow, and validate resonances with lattice QCD results. Overall, the study suggests nonperturbative resonance dynamics in the QGP can dominate heavy-flavor transport under RHIC-like conditions and shape experimental signals accordingly.

Abstract

Charm- and bottom-quark rescattering in a Quark-Gluon Plasma (QGP) is investigated with the objective of assessing the approach towards thermalization. Employing a Fokker-Planck equation to approximate the collision integral of the Boltzmann equation we augment earlier studies based on perturbative parton cross sections by introducing resonant heavy-light quark interactions. The latter are motivated by recent QCD lattice calculations which indicate the presence of "hadronic" states in the QGP. We model these states by colorless (pseudo-) scalar and (axial-) vector D- and B-mesons within a heavy-quark effective theory framework. We find that the presence of these states at moderate QGP temperatures substantially accelerates the kinetic equilibration of c-quarks as compared to using perturbative interactions. We also comment on consequences for $D$-meson observables in ultra-relativistic heavy-ion collisions.

Figures (5)

• Figure 1: Left panel: $c$($b$)-$q$ loop diagram representing the $D$($B$)-meson self-energy in the QGP. Right panel: "meson"-exchange diagrams contributing to the invariant matrix elements for the scattering of charm quarks on light quarks ($u$-channel) and anti-quarks ($s$-channel).
• Figure 2: Upper panel: drag coefficient $A$ (left) and diffusion coefficient $B_0$ (right) as a function of $c$-quark three-momentum at a temperature of $T=200$ MeV for various values of $\alpha_s$ (pQCD scattering) and $D$-meson widths (resonance exchanges). Lower panel: The same quantities as a function of temperature at fixed three-momentum $|\vec{p}|=0$.
• Figure 3: Left panel: Comparison of the friction coefficient for resonances with self-energies calculated in the renormalization scheme (\ref{['rencond']}) (solid line) and with form-factor regularization (dashed line). The coupling was chosen such that in both the resonance width $\Gamma$=0.4 GeV at the resonance mass. Right panel: The friction coefficient for different resonance masses as function of the temperature, evaluated in the form-factor regularization scheme.
• Figure 4: Left panel: equilibration time-scale $\tau=1/\gamma$ for charm and bottom quarks in the QGP as function of temperature with (solid and dashed line) and without (dash-dotted and dash-double-dotted lines) in-medium resonances. Right panel: consistency check of the dissipation-fluctuation relation, Eq. (\ref{['diss-fluct']}), for $c$-quarks with (solid line) and without (dash-dotted line) resonances, as well as for $b$-quarks (with resonances, dashed line), in the QGP.
• Figure 5: Left panel: results for the time-evolved $c$-quark $p_T$-spectra in the local rest frame with a temperature profile corresponding to QGP and mixed phase in central Au-Au collisions at $\sqrt{s_{NN}}$=200 GeV; dashed curve: initial spectrum taken from $p$-$p$ collisions; dash-dotted curve: final spectrum using pQCD cross sections only; solid curve: final spectrum using both pQCD and $D$-meson resonance interactions. Right panel: explicit time evolution in time steps of 1 fm/$c$ for the pQCD+resonance interactions.