Pion Valence-quark Parton Distribution Function

TL;DR

This paper calculates the pion valence-quark distribution function using Dyson-Schwinger equations, ensuring valence-quarks carry all momentum at the initial scale and analyzing its scaling behavior at higher energies.

Contribution

It introduces a corrected leading-order expression for the pion PDF within the Dyson-Schwinger framework, setting a consistent initial scale and analyzing its high-energy behavior.

Findings

Valence-quarks carry all pion momentum at initial scale

Pion PDF scales as (1-x)^{1.6} at high energy

Method provides a consistent nonperturbative calculation of pion structure

Abstract

Within the Dyson-Schwinger equation formulation of QCD, a rainbow ladder truncation is used to calculate the pion valence-quark distribution function(PDF). The gap equation is renormalized at a typical hadronic scale, of order 0.5GeV, which is also set as the default initial scale for the pion PDF. We implement a corrected leading-order expression for the PDF which ensures that the valence-quarks carry all of the pion's light-front momentum at the initial scale. The scaling behavior of the pion PDF at a typical partonic scale of order 5.2GeV is found to be $(1-x)^{\nu}$, with $\nu\simeq 1.6$, as $x$ approaches one.