Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations

TL;DR

This paper develops next-to-next-to-leading-order matching coefficients to connect lattice QCD calculations of quark correlation functions with parton distribution functions, enhancing the precision of hadronic structure extraction.

Contribution

It provides the first complete NNLO coefficient functions for matching lattice-calculable correlators to PDFs, enabling more accurate lattice-based hadron structure studies.

Findings

Reduced uncertainty in predictions with higher order matching coefficients

Derived matching coefficients for quasi-PDFs and pseudo-PDFs via Fourier transform

Method can be extended to sea-quark and gluon correlation functions

Abstract

We present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor non-singlet quark correlation functions in position space, which are calculable in lattice QCD, to parton distribution functions (PDFs). Using PDFs extracted from experimental data and our calculated matching coefficients, we predict valence-quark correlation functions that can be confronted by lattice QCD calculations. The uncertainty of our predictions is greatly reduced with higher order matching coefficients. By performing Fourier transformation, we also obtain matching coefficients for corresponding quasi-PDFs and pseudo-PDFs. Our method of calculations can be readily generalized to evaluate the matching coefficients for sea-quark and gluon correlation functions, putting the program to extract partonic structure of hadrons from lattice QCD calculations to be comparable with and complementary to that from experimental measurements.