Origin and Resummation of Threshold Logarithms in the Lattice QCD Calculations of PDFs

TL;DR

This paper develops a method to resum large threshold logarithms in lattice QCD calculations of PDFs, improving the theoretical accuracy of the matching coefficients and analyzing their impact on lattice results.

Contribution

It introduces a Mellin-moment space resummation technique for threshold logarithms in lattice QCD PDF calculations, accounting for DGLAP evolution and avoiding the Landau pole.

Findings

Resummation suppresses the PDF at large x.

Effect of threshold resummation is marginal within current data sensitivity.

Resummation formula is free from the Landau pole issue.

Abstract

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the DGLAP evolution, and we show that it can suppress the PDF at large $x$. Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large $x$.