Generalized parton distributions from the off-forward Compton amplitude in lattice QCD

A Hannaford-Gunn,P E L Rakow,J M Zanotti,K U Can,R D Young,G Schierholz,H Perlt,Cssm/Qcdsf/Ukqcd Collaborations ,R Horsley,Y Nakamura,H Stüben

doi:10.1103/physrevd.105.014502

Abstract

We determine the properties of generalised parton distributions (GPDs) from a lattice QCD calculation of the off-forward Compton amplitude (OFCA). By extending the Feynman-Hellmann relation to second-order matrix elements at off-forward kinematics, this amplitude can be calculated from lattice propagators computed in the presence of a background field. Using an operator product expansion, we show that the deeply-virtual part of the OFCA can be parameterised in terms of the low-order Mellin moments of the GPDs. We apply this formalism to a numerical investigation for zero-skewness kinematics at two values of the soft momentum transfer, $t = -1.1, -2.2 \;\text{GeV}^2$, and a pion mass of $m_{\pi}\approx 470\;\text{MeV}$. The form factors of the lowest two moments of the nucleon GPDs are determined, including the first lattice QCD determination of the $n=4$ moments. Hence we demonstrate the viability of this method to calculate the OFCA from first principles, and thereby provide novel constraint on the $x$- and $t$-dependence of GPDs.

Highlights

Since the 1990s, generalized parton distributions (GPDs) have been recognized as crucial observables in understanding hadron structure [1,2,3]
We determine the properties of generalized parton distributions (GPDs) from a lattice QCD calculation of the off-forward Compton amplitude (OFCA)
Using an operator product expansion, we show that the deeply virtual part of the OFCA can be parametrized in terms of the low-order Mellin moments of the GPDs

Summary

Introduction

Since the 1990s, generalized parton distributions (GPDs) have been recognized as crucial observables in understanding hadron structure [1,2,3]. They encode the spatial distribution of quarks and gluons in a fast-moving hadron [4]. Their Mellin moments contain information about the spin and orbital angular momentum of hadron constituents [2], which would resolve the decades-old “proton spin puzzle” [5,6]. Δ 1⁄4 P0 − P 1⁄4 q − q0: From these, we can form at most four linearly independent scalar variables: two scaling variables, ω ; θ −

Objectives

Results

Conclusion