# Solving the $\hat{q}$ puzzle with $x$ and scale dependence

## TL;DR

This paper proposes a novel approach to resolving the $$ puzzle by incorporating the dependence of $$ on parton momentum fraction $x$, scale $Q^2$, and temperature, supported by fits to experimental data.

## Contribution

It introduces the concept of a QGP parton distribution function (PDF) and demonstrates how scale evolution and $x$ dependence explain $$ variations across collision energies.

## Key findings

- QGP-PDF can be fitted to experimental data from PHENIX and CMS.
- Scale evolution of the QGP-PDF explains $$ enhancement at RHIC versus LHC.
- Inclusion of $x$ and $Q^2$ dependence resolves the $$ puzzle.

## Abstract

We present here a possible resolution of the jet quenching parameter $\hat{q}$ puzzle by exploring the momentum fraction $x$ and scale $Q^2$ dependence of $\hat{q}$, in addition to temperature dependence. We explore the momentum broadening of the jet due to Glauber gluon exchange with the quark-gluon plasma (QGP). This has led us to define the momentum fraction $x$ for the partons in the QGP. We also show here, for the first time, possible forms of the parton distribution function (PDF) of the QGP. The QGP-PDF as input in $\hat{q}$ has been used to fit the PHENIX and CMS data simultaneously. We observe that the scale evolution of the QGP-PDF and the energy of the jet are the missing ingredients responsible for the enhancement of $\hat{q}$ at the same temperature in RHIC collisions compared to LHC collisions.