Concerning pion parton distributions

Abstract

Analyses of the pion valence-quark distribution function (DF), $u^{\ddot{I}}€(x;\hat{I}\P )$, which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict $u^{\ddot{I}}€(x\simeq 1;\hat{I}\P )\sim (1-x{)}^{{\hat{I}}^2(\hat{I}\P )}$, ${\hat{I}}^2(\hat{I}\P \gtrsim m_p)>2$, where $m_p$ is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $x\simeq 1$ behaviour of $u^{\ddot{I}}€$, the empirical status remains uncertain because some methods used to fit existing data return a result for $u^{\ddot{I}}€$ 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.

15 pages, 9 figures, 1 table