Bjorken variable and scale dependence of quark transport coefficient in Drell-Yan process for proton incident on nucleus

TL;DR

This paper analyzes how the quark transport coefficient varies with the Bjorken variable and scale in the Drell-Yan process for proton-nucleus collisions, emphasizing nuclear geometry effects and proposing models for its dependence.

Contribution

It introduces a phenomenological analysis of the quark transport coefficient's dependence on kinematic variables in the nuclear Drell-Yan process, considering nuclear geometry effects.

Findings

Nuclear geometry significantly impacts the quark transport coefficient.

The quark transport coefficient varies with Bjorken variable and scale.

Differences in transport coefficient values are observed between E906 and E866 experiments.

Abstract

The Drell-Yan process for proton incident on nuclei is an excellent place for deeply studying the parton propagation in a nucleus. By means of the nuclear parton distributions determined only with lepton-nuclear deep inelastic scattering experimental data and the analytic parameterization of quenching weight based on BDMPS formalism, a phenomenological analysis of the nuclear Drell-Yan differential cross section ratio as a function of Feynman variable is performed from Fermilab E906 and E866 experimental data. With the nuclear geometry effect on nuclear Drell-Yan process and the quark transport coefficient as a constant, our predictions are in good agreement with the experimental measurements. It is found that nuclear geometry effect has a significant impact on the quark transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the nuclear Drell-Yan process. Our calculated results reveal that the difference in the values of quark transport coefficient exists from E906 and E866 experiments. However, confirming the conclusion that the quark transport coefficient depends on the target-quark momentum fraction, still need more accurate experimental data on the Drell-Yan differential cross section ratio in the future. Three models are proposed and discussed for the quark transport coefficient as a function of the measurable kinematic variables. The quark transport coefficient $\hat{q}$ is determined as a function of the Bjorken variable $x_2$ and scale $Q^2$. It is hoped that the parametrization form of quark transport coefficient in the cold nuclear medium can help to think about the parton propagation mechanism in nuclear matter.