Basic features of the pion valence-quark distribution function

TL;DR

This paper revises the calculation of the pion's valence-quark distribution, correcting previous flaws, and shows that valence quarks carry most of the pion's momentum with a distribution peaking at high x.

Contribution

It introduces a corrected, model-independent approach to determine the pion's valence-quark distribution, accounting for gluon contributions omitted in previous models.

Findings

Valence quarks carry about two-thirds of the pion's light-front momentum.

The valence-quark distribution behaves as (1-x)^2 near x~1.

Corrected models align better with experimental data.

Abstract

The impulse-approximation expression used hitherto to define the pion's valence-quark distribution function is flawed because it omits contributions from the gluons which bind quarks into the pion. A corrected leading-order expression produces the model-independent result that quarks dressed via the rainbow-ladder truncation, or any practical analogue, carry all the pion's light-front momentum at a characteristic hadronic scale. Corrections to the leading contribution may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we use an algebraic model to express the principal impact of both classes of corrections. This enables a realistic comparison with experiment that allows us to highlight the basic features of the pion's measurable valence-quark distribution, $q^\pi(x)$; namely, at a characteristic hadronic scale, $q^\pi(x) \sim (1-x)^2$ for $x\gtrsim 0.85$; and the valence-quarks carry approximately two-thirds of the pion's light-front momentum.