Suppression of the jet quenching parameter near the critical temperature

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 nonmonotonic $T$ 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 parametrized by a polynomial expression depending only on the background field. This expression is expected to be useful for phenomenological applications in jet physics.