Valence-quark distribution functions in the kaon and pion

TL;DR

This paper develops a framework for calculating valence-quark distribution functions in pions and kaons, incorporating gluon contributions and chiral symmetry breaking effects, and compares predictions with experimental data.

Contribution

It introduces a novel algebraic approach to include gluon and sea-quark effects in valence-quark distributions, improving upon the handbag approximation.

Findings

Valence quarks carry about 66% of pion momentum at the hadronic scale.

In the kaon, valence quarks carry approximately 95% of the momentum.

Predicted kaon-to-pion u-quark distribution ratio aligns with existing Drell-Yan data.

Abstract

We describe expressions for pion and kaon dressed-quark distribution functions that incorporate contributions from gluons which bind quarks into these mesons and hence overcome a flaw of the commonly used handbag approximation. The distributions therewith obtained are purely valence in character, ensuring that dressed-quarks carry all a meson's momentum at a characteristic hadronic scale and vanishing as $(1-x)^2$ when Bjorken-$x\to 1$. Comparing such distributions within the pion and kaon, it is apparent that the size of SU(3)-flavour symmetry breaking in meson parton distribution functions is modulated by the flavour dependence of dynamical chiral symmetry breaking. Corrections to these leading-order formulae may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we build an algebraic framework that is capable of expressing the principal impact of both classes of corrections. This enables a realistic comparison with experiment which allows us to identify and highlight basic features of measurable pion and kaon valence-quark distributions. We find that whereas roughly two-thirds of the pion's light-front momentum is carried by valence dressed-quarks at a characteristic hadronic scale, this fraction rises to 95% in the kaon; evolving distributions with these features to a scale typical of available Drell-Yan data produces a kaon-to-pion ratio of u-quark distributions that is in agreement with the single existing data set; and predict a u-quark distribution within the pion that agrees with a modern reappraisal of $\pi N$ Drell-Yan data. Precise new data are essential in order to validate this reappraisal and because a single modest-quality measurement of the kaon-to-pion ratio cannot be considered definitive.