Fluctuating heavy quark energy loss in a strongly coupled quark-gluon plasma

Results from an energy loss model that includes thermal fluctuations in the energy loss for heavy quarks in a strongly coupled plasma are shown to be qualitatively consistent with single particle data from both Relativistic Heavy Ion Collider and Large Hadron Collider. The model used is the first to properly include the fluctuations in heavy quark energy loss as derived in string theory and that do not obey the usual fluctuation-dissipation relations. These fluctuations are crucial for simultaneously describing both RHIC and LHC data; leading order drag results without fluctuations are falsified by current data. Including the fluctuations is nontrivial and relies on the Wong-Zakai theorem to fix the numerical Langevin implementation. The fluctuations lead to surprising results: $B$ meson anisotropy is similar to that for $D$ mesons at LHC, and the double ratio of $D$ to $B$ meson nuclear modification factors approaches unity more rapidly than even predictions from perturbative energy loss models. It is clear that future work in improving heavy quark energy loss calculations in AdS/CFT to include all energy loss channels is needed and warranted.

Figure 1

(a) The $p^x$-differential distribution of $m_c=1.5\mathrm{GeV}/{\mathrm{c}}^2$ charm quarks strongly coupled to a strongly coupled plasma in three spatial dimensions at $T=400\mathrm{MeV}$ which is moving at 0.9c in the $z$ direction. The effect of the thermal drag and fluctuations on the heavy quarks from strong coupling is found from implementing Eq. (1) using the Itô (pre-point), Stratonovich (mid-point), and Hänggi-Klimontovich (post-point) stochastic integrals. An implementation for which the fluctuation-dissipation theorem holds is also shown and compared to the result expected, the Jüttner distribution. (b) The same as (a) but for the $p^z$-differential distribution.

Figure 2

(Top) A comparison of FONLL predictions [46, 47, 48] for the electron spectrum from open heavy flavor production in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ to that measured by PHENIX [55]. (Bottom) Ratio of the PHENIX data to FONLL predictions; the solid black lines represent the uncertainty in the FONLL predictions due to scale variations. (Inset) Zoom in on the low-$p_T$ part of the ratio of data to FONLL predictions showing the full range of disagreement.

Figure 3

(a) Open heavy flavor electron $R_{AA}(p_T)$ at RHIC measured by PHENIX [55] and STAR [56] compared to predictions from heavy quark drag only (“leading order”) and heavy quark drag with fluctuations (“next-to-leading order”) energy loss models. (b) $D$ meson $R_{AA}(p_T)$ at LHC measured by ALICE [57] compared to the strongly coupled energy loss predictions. (c) Nonprompt $J/\psi$ meson $R_{AA}(p_T)$ at LHC measured by CMS [58] compared to the energy loss model predictions. For curves labeled ${\alpha }_s=0.3$, $\lambda =4\pi \times 0.3\times 3$ and $T_{\mathrm{SYM}}=T_{\mathrm{QCD}}$; for curves labeled $\lambda =5.5$, $T_{\mathrm{SYM}}=T_{\mathrm{QCD}}/3^{1/4}$.

Figure 4

$v_2(p_T)$ for $D$ mesons as measured by ALICE [61] at LHC compared to the predictions from the heavy quark energy loss model including fluctuations. For comparison the fluctuating energy loss model predictions for $B$ meson $v_2$ are also included. Curves labeled ${\alpha }_s=0.3$ use $\lambda =4\pi \times 0.3\times 3$ and $T_{\mathrm{SYM}}=T_{\mathrm{QCD}}$; curves labeled $\lambda =5.5$ have $T_{\mathrm{SYM}}=T_{\mathrm{QCD}}/3^{1/4}$.

Figure 5

The ratio of $D$ meson $R_{AA}(p_T)$ to $B$ meson $R_{AA}(p_T)$ from the strongly coupled heavy quark energy loss model at leading order (dashed) and including fluctuations (solid). Curves labeled ${\alpha }_s=0.3$ use $\lambda =4\pi \times 0.3\times 3$ and $T_{\mathrm{SYM}}=T_{\mathrm{QCD}}$; curves labeled $\lambda =5.5$ have $T_{\mathrm{SYM}}=T_{\mathrm{QCD}}/3^{1/4}$.