Heavy Quark Diffusion in Strong Magnetic Fields at Weak Coupling and Implications for Elliptic Flow

Kenji Fukushima; Koichi Hattori; Ho-Ung Yee; Yi Yin

doi:10.1103/PhysRevD.93.074028

paper

Heavy Quark Diffusion in Strong Magnetic Fields at Weak Coupling and Implications for Elliptic Flow

arXiv:1512.03689 · doi:10.1103/PhysRevD.93.074028

Abstract

We compute the momentum diffusion coefficients of heavy quarks, $κ_{∥}$ and $κ_{⊥}$ , in a strong magnetic field $B$ along the directions parallel and perpendicular to $B$ , respectively, at the leading order in QCD coupling constant $α_{s}$ . We consider a regime relevant for the relativistic heavy ion collisions, $α_{s} e B ≪ T^{2} ≪ e B$ , so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing light-quark mass limit, we find $κ_{⊥}^{LO} \propto α_{s}^{2} T e B$ in the leading order that arises from screened Coulomb scatterings with (1+1)-dimensional LLL quarks, while $κ_{∥}$ gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first non-zero leading order contributions to $κ_{∥}^{LO}$ come from the two separate effects: 1) the screened Coulomb scatterings with thermal gluons, and 2) a finite light-quark mass $m_{q}$ . The former leads to $κ_{∥}^{LO, gluon} \propto α_{s}^{2} T^{3}$ and the latter to $κ_{∥}^{LO, massive} \propto α_{s} (α_{s} e B)^{1/2} m_{q}^{2}$ . Based on our results, we propose a new scenario for the large value of heavy-quark elliptic flow observed in RHIC and LHC. Namely, when $κ_{⊥} ≫ κ_{∥}$ , an anisotropy in drag forces gives rise to a sizable amount of the heavy-quark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid.

30 page. 5 figures. Explanations improved; Typos corrected; Published in Phys. Rev. D

Heavy Quark Diffusion in Strong Magnetic Fields at Weak Coupling and Implications for Elliptic Flow

Abstract

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