Classical strongly coupled quark-gluon plasma. VII. Energy loss

We use linear response analysis and the fluctuation-dissipation theorem to derive the energy loss of a heavy quark in the SU($2$) classical Coulomb plasma in terms of the $l=1$ monopole and nonstatic structure factor. The result is valid for all Coulomb couplings $\Gamma =V/K$, the ratio of the mean potential to kinetic energy. We use the Liouville equation in the collisionless limit to assess the SU($2$) nonstatic structure factor. We find the energy loss to be strongly dependent on $\Gamma$. In the liquid phase with $\Gamma \approx 4$, the energy loss is mostly metallic and soundless with neither a Cerenkov nor a Mach cone. Our analytical results compare favorably with the SU($2$) molecular dynamics simulations at large momentum and for heavy quark masses.

Figure 1

Static structure factors for $\Gamma =2,3,4$.

Figure 2

${\mathbf{S}}_{01}(q)$: molecular dynamics simulation (a) and analytical (b). See text for details.

Figure 3

Surface plot of $-v^2\mathit{dK}/\mathit{drdxdq}$ for charm (left panel) and bottom (right panel). See text for details.

Figure 4

$-v^2\mathit{dK}/\mathit{drdxdq}$ versus $v/v_T$ for charm (left panel) and bottom (right panel) quark for fixed $q$. See text for details.

Figure 5

Energy loss for charm (a) and bottom (b) in the cQGP: $\Gamma =2,3,4$. Figure (c) shows the plot of the dimensionless shear viscosity when $\Gamma =2$, 3, and 4 (dots on the solid curve). See text for details.

Figure 6

Logarithmic energy loss for charm (a), bottom (b), and both (c) in absolute units. See text for details.

Figure 7

Energy loss for charm (a), bottom (b), and heavy (c) quarks: analytical (dotted curve) versus SU(2) molecular dynamics [19] (solid curve with error bars).