Pion generalized parton distribution from lattice QCD

Jiunn-Wei Chen,Huey-Wen Lin,Jian-Hui Zhang

doi:10.1016/j.nuclphysb.2020.114940

Abstract

We present the first lattice calculation of the valence-quark generalized parton distribution (GPD) of the pion using the large-momentum effective theory (LaMET) approach. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken x and the transverse impact-parameter distributions. Our calculation is done using clover valence fermions on an ensemble of gauge configurations with 2+1+1 flavors (degenerate up/down, strange and charm) of highly improved staggered quarks (HISQ) with lattice spacing a≈0.12 fm, box size L≈3 fm and pion mass mπ≈310 MeV. The parton distribution function and the form factor are reproduced as special limits of the GPD as expected. Due to the large errors, this exploratory study does not show a clear preference among different model assumptions about the kinematic dependence of the GPD. To discriminate between these assumptions, future studies using higher-statistics data will be crucial.

Highlights

In the past few decades, extensive studies of parton distribution functions (PDFs) have provided us with detailed knowledge of the longitudinal momentum distribution of quarks and gluons, and, a one-dimensional picture of hadrons
As the generalized parton distribution (GPD) usually contribute to experimental observables through convolutions and they have more complicated kinematic dependence than the PDFs, extracting the GPDs from these experimental measurements is in general rather difficult
We present our numerical results for the valence-quark GPD in the pion

Summary

Introduction

In the past few decades, extensive studies of parton distribution functions (PDFs) have provided us with detailed knowledge of the longitudinal momentum distribution of quarks and gluons, and, a one-dimensional picture of hadrons. To map out the multidimensional partonic structure of hadrons, which is an important goal for experiments carried out at the existing facilities in DESY, JLab, BNL, CERN or the planned Electron-Ion Collider, we need to study quantities exhibiting the transverse structure of hadrons One such quantity that has attracted a lot of interest in the past few years are the generalized parton distributions (GPDs) [1,2,3]. A new theory framework has been developed that allows for lattice calculations of the x-dependence, instead of the moments, of parton quantities [17,18] This theory is known as the large-momentum effective theory (LaMET). Our calculation is done using clover valence fermions on an ensemble of gauge configurations with 2 + 1 + 1 flavors (degenerate up/down, strange and charm) of highly improved staggered quarks (HISQ) [87] generated by the MILC Collaboration [88] with lattice spacing a ≈ 0.12 fm, box size L ≈ 3 fm and pion mass mπ ≈ 310 MeV

From quasi-GPD to GPD in the pion

Lattice calculation setup

Numerical results and discussion

Summary