Unpolarized and Helicity Generalized Parton Distributions of the Proton within Lattice QCD.

Extended Twisted Mass Collaboration ,Constantia Alexandrou,Martha Constantinou,Krzysztof Cichy,Aurora Scapellato,Karl Jansen,Kyriakos Hadjiyiannakou,Fernanda Steffens

doi:10.1103/physrevlett.125.262001

Abstract

We present the first calculation of the x dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-moving protons coupled to nonlocal operators containing a Wilson line. We present results for proton momenta 0.83,1.25,1.67GeV, and momentum transfer squared 0.69,1.38 GeV^{2}. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate mass light quarks, a strange quark, and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the MS[over ¯] scheme at a scale of 2GeV.

Highlights

We present the first calculation of the x dependence of the proton generalized parton distributions (GPDs) within lattice QCD
These studies led to the realization that high-energy scattering processes can be factorized into perturbative and nonperturbative parts. The latter includes information about the parton structure of the proton [1]. This resulted in the introduction of a complete set of key quantities, namely the parton distribution functions (PDFs) [1], generalized parton distributions (GPDs) [2,3,4], and transverse momentum dependent distributions (TMDs) [5,6]
For H GPD and H GPD at ξ 1⁄4 0, we find that the momentum dependence is small and within the reported uncertainties

Summary

Introduction

Unpolarized and Helicity Generalized Parton Distributions of the Proton within Lattice QCD We present the first calculation of the x dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-moving protons coupled to nonlocal operators containing a Wilson line.

Results

Conclusion