Quasiparton distribution functions at NNLO: Flavor nondiagonal quark contributions

Long-Bin Chen,Ruilin Zhu,Wei Wang

doi:10.1103/physrevd.102.011503

Abstract

We present a next-to-next-to-leading order (NNLO) calculation of the quasiparton distribution functions (quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor nondiagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.

Highlights

Understanding the underlying structure of nucleons from degrees of quarks and gluons has been a long-standing goal in hadron physics
The goal of this paper is to go beyond the one-loop order and perform, for the first time, a two-loop computation of the quasi-parton distribution functions (PDFs) in the large momentum effective theory (LaMET), taking the nondiagonal quark-quark channel as an example
This channel starts at two-loop order, which allows us to demonstrate the factorization in an intuitive method

Summary

INTRODUCTION

Understanding the underlying structure of nucleons from degrees of quarks and gluons has been a long-standing goal in hadron physics. An effective theory, called large momentum effective theory (LaMET) [11,12], has been developed to compute various parton distribution functions on lattice In this framework, an appropriate static-operator matrix element (quasiobservable) that approaches the parton observable in the infinite momentum limit of the external hadron is constructed. The goal of this paper is to go beyond the one-loop order and perform, for the first time, a two-loop computation of the quasi-PDF in the LaMET, taking the nondiagonal quark-quark channel as an example This channel starts at two-loop order, which allows us to demonstrate the factorization in an intuitive method. We notice that recently, the renormalization of quasi-PDF operators have been studied at two-loop order [22,23] Together with this result, our paper will provide an important step toward a complete two-loop calculation of quasi-PDF and the associated matching coefficients.

FACTORIZATION AT TWO-LOOP ORDER

MATCHING COEFFICIENT AT TWO-LOOP ORDER

CONCLUSION