Directional dead-cone effect in QCD matter

Abstract

We consider the propagation of heavy quarks through a dense, hydrodynamically flowing QCD medium, representative of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Working in the high-energy limit, we identify two novel mass-dependent effects arising from the heavy quark coupling to the local medium flow. The first is the emergence of a tensorial jet transport coefficient, $\hat{q}_{ij}$, which encodes the directional structure of transverse-momentum broadening. The second, named the directional dead-cone effect, corresponds to an anisotropic suppression of medium-induced radiation aligned with the hydrodynamic flow. We discuss how these effects manifest in jet observables and identify distinctive signature of heavy quark dynamics in an evolving medium.

Figures (4)

• Figure 1: Heavy quark propagation in a flowing medium with velocity $u^\mu$. Momentum broadening takes a tensorial character, introduced via $\hat{q}_{ij}$; homogeneous diffusion is recovered in the massless quark limit. A directional dead-cone angle $\Theta_{\rm dc}$ leads to a modulation of the dead-cone geometry and medium induced radiation pattern inside.
• Figure 2: Amplitude for the evolution of a single heavy quark in the presence of a flowing medium with velocity $u^\mu$. The lower line indicates that, to the accuracy considered here, the amplitude can be cast as a convolution of the initial quark current $J$ and a time-like Wilson line $W$, now dependent on the background flow field.
• Figure 3: Amplitude entering inclusive single gluon production in the presence of a flowing medium with velocity $u^\mu$. Bottom diagram depicts the decomposition of the amplitude at the leading sub-eikonal order, where all flow effects can be absorbed into the vertex and fermionic lines.
• Figure 4: The medium-induced spectrum off a heavy quark in flowing matter, given by Eq. \ref{['eq:spec_final']}, is shown for three gluon energies, $\omega = 0.06\,\omega_c$, $\omega = 0.12\,\omega_c$ and $\omega = 0.20\,\omega_c$, as a function of the gluon emission angle with respect to the heavy quark direction $\sin\theta\simeq\sqrt{2}\frac{|{\boldsymbol k}|}{\omega}$. For each gluon energy, three different curves are plotted: the solid line shows the spectrum with ${\boldsymbol k}$ and ${\boldsymbol u}$ orthogonal ($\phi=\frac{\pi}{2}$) in the transverse plane, while the dash-dotted and dashed lines correspond to them being parallel ($\phi =0$) and anti-parallel ($\phi =\pi$) respectively. The magnitude of the transverse flow and the heavy quark mass are fixed at $|{\boldsymbol u}| =0.7$ and $m_{Q}=4$ GeV, as well as the jet quenching parameter $\hat{q}_0 = 1\,\text{GeV}^2\cdot\text{fm}^{-1}$, while $L$ and $E$ are varied in the three different panels.