Jet energy loss in anisotropic plasmas meets limiting attractors

Abstract

We consider the energy loss of a high-energy parton in the early anisotropic plasma in heavy-ion collisions. Working in the harmonic approximation, we compute the change in the mean energy of an emitted gluon in the presence of an anisotropic background, characterized by anisotropic jet quenching parameters $\hat q_{x}\neq \hat q_{y}$. Evaluating the resulting integrals numerically, we compare with isotropic media, and obtain a simple pocket formula to estimate the impact of anisotropy on the mean emitted gluon energy, which is generally small. We then combine our results with the values of the jet quenching parameter extracted from QCD kinetic theory simulations and show that the medium length dependence of this mean energy loss exhibits the characteristics of limiting attractors, which can be obtained by extrapolating to zero and infinite coupling. Our study thus relates energy loss of jet partons to universal dynamics of anisotropic plasmas.

Figures (11)

• Figure 1: Relative difference between isotropic and anisotropic energy loss $\Delta E/E_{\mathrm{iso}} =\frac{E_\text{aniso} - E_\text{iso}}{E_\text{iso}}$ as a function of anisotropy $\Delta\hat{q}/\hat{q}$. The fit using Eq. \ref{['pocket-formula']} is depicted as a dashed line. The anisotropic energy loss $E_\mathrm{aniso}$ is generally smaller than $E_\mathrm{iso}.$ For maximum anisotropy $\Delta\hat{q}/\hat{q} = 1$ we find $\Delta E/E \approx -6\%$.
• Figure 2: Difference $\Delta Q = Q_\text{aniso}-Q_\text{iso}$ of the quenching weight in an anisotropic ($Q_\text{aniso}$) and corresponding isotropic system ($Q_\text{iso}$) as a function of $p_\perp/(n\omega_c)$. The anisotropy effects decrease with increasing rescaled momentum. The inset shows the quenching weight in an isotropic system, which converges to $Q_{\rm iso}\to1$ for large $p_\perp/(n\omega_c)$.
• Figure 3: Comparison between the effective jet quenching parameters $\hat{q}_x^\text{eff}/\hat{q}_y^\text{eff}$ (solid lines) as well as the instantaneous jet quenching parameters $\hat{q}_x/\hat{q}_y$ (dashed lines) for various couplings $\lambda$. The curves indicate larger anisotropy at earlier times together with a "turning point", where the curves pass from $\hat{q}_x > \hat{q}_y$ to $\hat{q}_x < \hat{q}_y$, and similar for $\hat{q}_x^\mathrm{eff}/\hat{q}_y^\mathrm{eff}$. The time axis is rescaled with the bottom-up timescale $\tau_{\mathrm{BMSS}}$, i.e., $\tilde{v}=\tau/\tau_{\mathrm{BMSS}}$ (Eq. \ref{['eq:time-rescaling']}). We also show the limiting weak-coupling attractor \ref{['eq:limiting-attractor-general-weak']} as a black curve denoted by $\lambda \to 0$.
• Figure 4: The ratio of the effective jet quenching parameters $\hat{q}_x^\mathrm{eff}/\hat{q}^\mathrm{eff}_y$ for fixed rescaled times $\tilde{v}=\tau/\tau_{\mathrm{BMSS}}$. We also show the linear extrapolation to the weak-coupling limiting attractor \ref{['eq:limiting-attractor-general-weak']}.
• Figure 5: Quenching weight $Q$ as a function of $p_\perp$ for $\lambda=10$ for various fixed medium sizes $L$. For smaller medium sizes, the convergence to $1$ goes more rapidly. The inset shows $\Delta Q=Q_\text{aniso}-Q_\text{iso}$ as a function of medium size $L$ for various transverse momenta $p_\perp$. The impact of the anisotropy mostly increases with larger medium sizes.