Heavy Quark Diffusion from $2+1$ Flavor Lattice QCD with 320 MeV Pion Mass

We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks corresponding to a pion mass of around 320 MeV. For temperatures $195\mathrm{MeV}<T<352\mathrm{MeV}$, the heavy quark spatial diffusion coefficient is found to be significantly smaller than previous quenched lattice QCD and recent phenomenological estimates. The result implies very fast hydrodynamization of heavy quarks in the quark-gluon plasma created during ultrarelativistic heavy-ion collision experiments.

Figure 1

The chromoelectric correlator normalized by its weak-coupling structure at tree level ($G^{\mathrm{norm}}$) as a function of $\tau$ calculated on the ${96}^3\times N_{\tau }$ lattices (open symbols) and ${64}^3\times 20$ lattices (filled symbols) at two different flow times in units of $\tau$.

Figure 2

The continuum and zero flow time extrapolated results for the chromoelectric correlator at different temperatures as a function of $\tau T$. Also shown is the result for the highest temperature at nonzero lattice spacing corresponding to $N_{\tau }=20$ and flow time $\sqrt{8{\tau }_{\mathrm{F}}}/\tau =0.3$. The dashed lines indicate fitted model correlators for the “smax” model using the NLO ${\rho }_{\mathrm{UV}}$.

Figure 3

The spatial heavy quark diffusion coefficient in units of $2\pi T$ from our lattice calculations compared to the $\mathrm{AdS}/\mathrm{CFT}$ estimate [6], NLO perturbative calculation [5], and the quenched lattice QCD calculations [16, 18, 24]. For the quenched lattice data we show the result of Ref. [18] for $T=1.1T_c$, the result of Ref. [16] for $T=1.5T_c$, and the results of Ref. [24] for the remaining temperatures. For the NLO calculations we used two values of the renormalization scale, $\mu =2\pi T$ (lower dashed line) and $\mu =4\pi T$ (upper dashed line). Also shown are the phenomenological estimates [48, 49, 50, 51], see main text.