The energy and scale dependence of $\hat{q}$ and the JET puzzle

We present an attempt to probe the underlying structure of the quark-gluon plasma (QGP) at high resolution, based on the extracted jet transport coefficient $\hat{q}$. We argue that the exchanged momentum $k$ between the hard parton and the medium varies over a range of scales, and for $k\geq$ 1 GeV, $\hat{q}$ can be expressed in terms of a parton distribution function (PDF). Because the mass of a QGP constituent is unknown, we define a scaling variable $x_N$ to represent the ratio of the parton momentum to the momentum of a self-contained section of the plasma which has a mass of 1 GeV. This scaling variable is used to parametrize the QGP-PDF. Calculations, based on this reconstructed $\hat{q}$ are compared to data sensitive to the hardcore of jets $i.e.,$ the single hadron suppression in terms of the nuclear modification factor $R_{AA}$ and the azimuthal anisotropy parameter $v_{2}$, as a function of transverse momentum $p_{\mathrm{T}}$, centrality and energy of the collision. It is demonstrated that the scale evolution of the QGP-PDF is responsible for the reduction in the normalization of $\hat{q}$ between fits to Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) data; a puzzle, first discovered by the JET collaboration.