Extracting parton distribution functions from lattice QCD calculations

Yan-Qing Ma,Jian-Wei Qiu

doi:10.1103/physrevd.98.074021

Abstract

Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and quarks and gluons within it. We propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD calculations of good "lattice cross sections", which are basically single-hadron matrix elements that are lattice QCD calculable and perturbative QCD factorizable into the PDFs. To demonstrate the existence of good "lattice cross sections", we take quasi-quark distribution introduced by Ji [1] as a case study to show that it could be factorized into the PDFs to all orders in perturbation theory if it can be multiplicatively renormalized. We calculate the factorized coefficients at the next-to-leading order in $\alpha_s$.

Highlights

Quantum chromodynamics (QCD) is believed to be the fundamental theory for strong interactions and is responsible for holding the quarks and gluons together to form nucleons and nuclei, the core of all visible matter in the Universe
Since quasiquark distribution is calculable in lattice QCD (LQCD) and its renormalizability has been well studied in Refs. [11,12,13], we show below that quasiquark distribution can be EXTRACTING PARTON DISTRIBUTION FUNCTIONS FROM
One first generates “data” from LQCD calculation of good lattice cross sections” (LCSs) and extracts Parton distribution functions (PDFs) by QCD global analysis of these data, similar to what has been done for extracting PDFs with experimental data

Summary

INTRODUCTION

Quantum chromodynamics (QCD) is believed to be the fundamental theory for strong interactions and is responsible for holding the quarks and gluons (or, in general, partons) together to form nucleons and nuclei, the core of all visible matter in the Universe. We propose a rigorous program to extract PDFs from good “time-independent” and LQCD calculable hadronic matrix elements, defined with equal-time operators, that can be factorized into the desired PDFs in the same spirit of QCD factorization of experimental cross sections. Our proposed program to extract PDFs from LQCD calculable LCSs could be extended for extracting other parton distributions and correlation functions by constructing new LCSs, including matrix elements made of two states of different momenta This program could provide new opportunities to explore the partonic structure of hadrons, such as free neutron or various mesons, which are difficult to do scattering experiments with. Factorized to PDFs with perturbatively calculable coefficients to all orders in QCD perturbation theory

QUASI-PDFs AND FACTORIZATION

COEFFICIENT FUNCTIONS AT NLO

SUMMARY