Multiple Parton Scattering in Nuclei: Modified DGLAP Evolution for Fragmentation Functions

TL;DR

This paper develops and numerically solves medium-modified DGLAP evolution equations for fragmentation functions in nuclear matter, incorporating multiple parton scattering and gluon fusion, and compares results with experimental data to extract the jet transport parameter.

Contribution

It extends the medium-modified DGLAP framework to include gluon scattering and quark-antiquark production, providing a more comprehensive description of parton energy loss in nuclei.

Findings

Numerical solutions show dependence of fragmentation functions on $Q^2$, $E$, $L$, and $ abla q$.

Extracted jet transport parameter $ abla q_{0}=0.024 ext{ GeV}^2/ ext{fm}$ from data.

Modified fragmentation functions agree with experimental DIS data on large nuclei.

Abstract

Within the framework of generalized factorization of higher-twist contributions to semi-inclusive cross section of deeply inelastic scattering off a large nucleus, multiple parton scattering leads to an effective medium-modified fragmentation function and the corresponding medium-modified DGLAP evolution equations. We extend the study to include gluon multiple scattering and induced quark-antiquark production via gluon fusion . We numerically solve these medium-modified DGLAP (mDGLAP) evolution equations and study the scale ($Q^2$), energy ($E$), length ($L$) and jet transport parameter ($\hat q$) dependence of the modified fragmentation functions for a jet propagating in a uniform medium with finite length (a "brick" problem). We also discuss the concept of parton energy loss within such mDGLAP evolution equations and its connection to the modified fragmentation functions. With a realistic Wood-Saxon nuclear geometry, we calculate the modified fragmentation functions and compare to experimental data of DIS off large nuclei. The extracted jet transport parameter at the center of a large nucleus is found to be $\hat q_{0}=0.024\pm0.008$ GeV$^{2}$/fm.