title: The asymptotic behaviour of parton distributions at small and largex.
abstract: It has been argued from the earliest days of quantum chromodynamics that at asymptotically small values ofxthe parton distribution functions (PDFs) of the proton behave as [Formula: see text], where the values of [Formula: see text] can be deduced from Regge theory, while at asymptotically large values ofxthe PDFs behave as [Formula: see text], where the values of [Formula: see text] can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents [Formula: see text] and [Formula: see text] from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio [Formula: see text] at largex, and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.
authors.affiliation: The Higgs Centre for Theoretical Physics, University of Edinburgh, JCMB, KB, Mayfield Rd., Edinburgh, EH9 3JZ Scotland.
authors.forename: Richard D
authors.initials: RD
authors.lastname: Ball
authors.affiliation: Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP UK.
authors.forename: Emanuele R
authors.initials: ER
authors.lastname: Nocera
authors.affiliation: Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP UK.
authors.forename: Juan
authors.initials: J
authors.lastname: Rojo