Suppression of the jet quenching parameter near the critical temperature

TL;DR

The paper addresses how the jet quenching parameter ${\hat q}$ behaves near the QCD critical temperature, where nonperturbative effects become important. It develops a background-field effective theory for a semi-QGP with a temperature-dependent ${\cal Q}$ that modifies parton distributions and HTL propagators, and derives a gauge-invariant expression for ${\hat q}$ incorporating both off-diagonal and diagonal color contributions. Numerically, ${\hat q}/T^3$ is found to be dramatically suppressed near $T_d$ due to ${\cal Q}$, with the suppression captured by a polynomial in the background field and showing qualitative agreement with lattice data; running coupling introduces a non-monotonic temperature dependence at higher $T$. The work provides a practical phenomenological tool via a polynomial parameterization of the ${\hat q}$-ratio, enabling incorporation of semi-QGP effects into jet-physics analyses across the deconfinement transition.

Abstract

In this work, we study the jet quenching parameter ${\hat q}$ by using a background field effective theory. Particular attention is paid to its behavior near the critical temperature where nonperturbative effects induced by the deconfining phase transition are taken into account through a self-consistently introduced background field ${\cal Q}$. We adopt a theoretical approach in which the interaction rate between the energetic jet and medium partons is computed diagrammatically and the hard-thermal-loop resummed propagator is used to regulate the infrared divergence. In the presence of a background field, its influence on the jet quenching parameter manifests in two aspects. One is the modification on the screening mass in the resummed propagator, which leads to an enhanced ${\hat q}$. The other corresponds to the ${\cal Q}$-modified parton distribution function which is dominant and leads to a suppression of ${\hat q}$. Decreasing the temperature $T$, our result shows a non-monotonic $T$-dependence of the dimensionless ${\hat q}/T^3$. In the high temperature region, ${\hat q}/T^3$ shows an increase with decreasing $T$ due to the running coupling effect. Near the critical temperature, the background field plays a significant role and a dramatic suppression of ${\hat q}/T^3$ is found which qualitatively agrees with the Lattice simulation. In addition, the background field modification on the jet quenching parameter which is characterized by the ${\hat q}$-ratio can be simply parameterized by a polynomial expression depending only on the background field. This expression is expected to be useful for phenomenological applications in jet physics.

Figures (5)

• Figure 1: The dimensionless $\hat{q}$ as a function of $\lambda_\perp/T$ at $\Lambda_\perp/T=10$. The left plot shows the comparison for contributions linear in the distribution function obtained from Eq. (\ref{['qh']}) and Eq. (\ref{['qhat']}) at different gauge couplings. The right plot shows the corresponding comparison for contributions quadratic in the distribution function. ${\hat{q}}^{\rm ex}_{\rm hard2}$ presents the result obtained beyond the approximation used in ${\hat{q}}_{\rm hard2}$. See text for a more detailed discussion.
• Figure 2: The dimensionless $\hat{q}$ as a function of $\Lambda_\perp/T$ for two different gauge couplings. We plot the results from Eq. (\ref{['qhat']}) and those obtained based on the simplified $|{\cal M}|^2$ as used in Ref. Boguslavski:2024jwr. In addition, the soft limit of ${\hat{q}}$ as given in Eq. (\ref{['qs']}) is also shown for comparison.
• Figure 3: The dimensionless jet quenching parameter in a background field as a function of the cutoff $\Lambda_\perp/T$ (left) and the temperature $T/T_d$ (right). We use the fixed gauge coupling and also show the corresponding result at ${\cal Q}=0$ for comparison.
• Figure 4: The ratio of the jet quenching parameter with and without the background field. Left: the cutoff dependence for different temperatures with the gauge coupling fixed. Right: the temperature dependence for different coupling constants with the cutoff fixed.
• Figure 5: The jet quenching parameter with running coupling effect. Left: The temperature dependence of the dimensionless ${\hat{q}}/T^3$ with and without ${\cal Q}$. The partial modification due to the background field is also shown. See text for more details. Right: The temperature dependence of the ${\hat{q}}$-ratio.