Nuclear parton distribution functions and their uncertainties

Abstract

We analyze experimental data of nuclear structure-function ratios ${F}_{2}^{A}∕{F}_{2}^{{A}^{\ensuremath{'}}}$ and Drell-Yan cross section ratios for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Valence-quark distributions are determined by the ${F}_{2}$ data at large $x$; however, the small-$x$ part is not obvious from the data. On the other hand, the antiquark distributions are determined well at $x\ensuremath{\sim}0.01$ from the ${F}_{2}$ data and at $x\ensuremath{\sim}0.1$ by the Drell-Yan data; however, the large-$x$ behavior is not clear. Gluon distributions cannot be fixed by the present data and they have large uncertainties in the whole $x$ region. Parametrization results are shown in comparison with the data. We provide a useful code for calculating nuclear PDFs at given $x$ and ${Q}^{2}$.