Pion parton distribution functions from lattice QCD

TL;DR

This paper presents lattice QCD calculations of pion parton distribution functions, addressing finite volume effects, renormalization, and extrapolation to connect with experimental data.

Contribution

It provides the first detailed investigation of finite volume effects on the pion matrix element and non-perturbative renormalization for lattice QCD calculations of PDFs.

Findings

Finite volume effects are surprisingly large.

Non-perturbative renormalization enables comparison with experiments.

Results include continuum limit extrapolation and discussion of uncertainties.

Abstract

We report on recent results for the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. For the first time finite volume effects of this matrix element are investigated and come out to be surprisingly large. We use standard Wilson and non-perturbatively improved clover actions in order to control better the extrapolation to the continuum limit. Moreover, we compute, fully non-perturbatively, the renormalization group invariant matrix element, which allows a comparison with experimental results in a broad range of energy scales. Finally, we discuss the remaining uncertainties, the extrapolation to the chiral limit and the quenched approximation.