Determination of nuclear parton distribution functions and their uncertainties at next-to-leading order

Nuclear parton distribution functions (NPDFs) are determined by global analyses of experimental data on structure-function ratios F₂A/F₂^A' and Drell-Yan cross-section ratios σDYA/σDY^A'. The analyses are done in the leading order (LO) and next-to-leading order (NLO) of running coupling constant αₛ. Uncertainties of the NPDFs are estimated in both LO and NLO for finding possible NLO improvement. Valence-quark distributions are well determined, and antiquark distributions are also determined at $x<0.1$. However, the antiquark distributions have large uncertainties at $x>0.2$. Gluon modifications cannot be fixed at this stage. Although the advantage of the NLO analysis, in comparison with the LO one, is generally the sensitivity to the gluon distributions, gluon uncertainties are almost the same in the LO and NLO. It is because current scaling-violation data are not accurate enough to determine precise nuclear gluon distributions. Modifications of the PDFs in the deuteron are also discussed by including data on the proton-deuteron ratio F₂D/F₂ᵖ in the analysis. A code is provided for calculating the NPDFs and their uncertainties at given x and Q² in the LO and NLO.