Concerning pion parton distributions

TL;DR

This paper discusses the theoretical expectations and experimental uncertainties in the pion's valence-quark distribution, emphasizing the need for new precise data to resolve current discrepancies and test QCD predictions.

Contribution

It introduces an all-orders exact evolution scheme for parton distribution functions based on an effective charge, providing a new tool to analyze pion structure data.

Findings

Predicted ${u}^ extpi(x o 1) o (1-x)^{eta( ext{ extzeta})}$ with $eta > 2$

Current experimental data are inconsistent with QCD-based predictions

A new evolution scheme for parton DFs is proposed and tested

Abstract

Analyses of the pion valence-quark distribution function (DF), ${u}^\pi(x;\zeta)$, which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict ${u}^\pi(x\simeq 1;\zeta) \sim (1-x)^{\beta(\zeta)}$, $\beta(\zeta \gtrsim m_p)>2$, 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 ${u}^\pi$, the empirical status remains uncertain because some methods used to fit existing data return a result for ${u}^\pi$ 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.