Uncertainties of Parton Distribution Functions

High-energy particles interact through their quark and gluon constituents—the partons. By the asymptotic freedom of QCD, the parton cross sections may be approximated by perturbation theory. Then by the factorization theorem of QCD, the parton distribution functions of hadrons are the link between perturbative QCD and experimental measurements. This theory applies to a variety of high-energy processes, including deep-inelastic lepton scattering from nucleons (DIS), Drell-Yan production of μμ pairs in nucleon-nucleon collisions (DY), and production of high-pT jets at pp̄ or pp colliders. The parton distribution functions (PDFs) are important in high-energy physics. Any scattering experiment with nucleons in the initial state will require PDFs for the analysis and interpretation of the experiment. Currently, the HERA accelerator experiments measure ep and ep scattering; the Tevatron collider creates pp collisions. Tests of the standard model and the search for new physics rely on PDF phenomenology. QCD global analysis has several goals: to construct an accurate set of PDFs; to know the uncertainties of the PDFs, which come from experimental measurement errors and from theoretical approximations; and to enable predictions, with realistic uncertainties, for future experiments. The full, systematic study of PDF uncertainties developed slowly [1, 2]. The first practical parton distributions with full error bands were produced by Botje [3] using DIS data. Today many groups and individuals are involved in this active field of research. Both the CTEQ group [4] and the MRST group [5] have provided complete uncertainty analyses of their PDFs; the PDFs from these groups are widely used in highenergy physics. The HERA collaborations, ZEUS [6] and H1 [7], have constructed PDF models based on their own data, including error bands. Other individuals have made important contributions [8, 9]; and the Fermilab group [10] has developed a new methodology for PDFs by Monte Carlo sampling in the parton function space. This paper will discuss several issues, focusing on the CTEQ methods and results. Section 2 describes the CTEQ input. Section 3 concerns the treatment of systematic errors. Section 4 discusses the compatibility of different data sets within a global fit to data. Section 5 explains the CTEQ uncertainty analysis.