Multiple parton scattering in nuclei: Modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution for fragmentation functions

Abstract

Within the framework of generalized factorization of higher-twist contributions to semi-inclusive cross sections of deeply inelastic scattering (DIS) 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 ($\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}$) 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 them to experimental data on DIS off large nuclei. The extracted jet transport parameter at the center of a large nucleus is found to be ${\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}}_{0}=0.024\ifmmode\pm\else\textpm\fi{}0.008$ GeV${}^{2}$/fm.