Extraction of Next-to-Next-to-Leading-Order Parton Distribution Functions from Lattice QCD Calculations

We present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor nonsinglct 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, making the program to extract partonic structure of hadrons from lattice QCD calculations comparable with and complementary to that from experimental measurements.

Automated summary

This study introduces complete next-to-next-to-leading-order coefficient functions to match flavor nonsinglct quark correlation functions in position space to parton distribution functions (PDFs), making predictions for valence-quark correlation functions. By performing Fourier transformation, matching coefficients for corresponding quasi-PDFs and pseudo-PDFs are obtained. The calculations can be generalized to evaluate matching coefficients for sea-quark and gluon correlation functions.