Concerning pion parton distributions

Abstract

Analyses of the pion valence-quark distribution function (DF), uπ (x; ζ ), which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict uπ (x 1; ζ ) ∼ (1 − x)β(ζ ), β(ζ m p) > 2, where m p is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the x 1 behaviour of uπ , the empirical status remains uncertain because some methods used to fit existing data return a result for uπ that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated