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

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.

20 pages, 7 figures

References in corpus (9)

• Transverse spin structure of the nucleon from lattice QCD simulations
• Dispersion representations for hard exclusive processes
• Dispersion relations and subtractions in hard exclusive processes
• Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering
• Moments of nucleon generalized parton distributions from lattice QCD
• Longitudinal target-spin asymmetries for deeply virtual Compton scattering
• Nucleon Compton scattering in the Dyson-Schwinger approach
• Some numerical studies of the evolution of generalized parton distributions
• A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators

Cited by in corpus (16)

• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks
• Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO
• Continuum limit of parton distribution functions from the pseudo-distribution approach on the lattice
• Moments of Axial-Vector GPD from Lattice QCD: Quark Helicity, Orbital Angular Momentum, and Spin-Orbit Correlation
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions
• Constraining beyond the Standard Model nucleon isovector charges
• Exploring Baryon Resonances with Transition Generalized Parton Distributions: Status and Perspectives
• Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD
• Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
• Mapping Parton Distributions of Hadrons with Lattice QCD
• Accessing Compton Form Factors at the Electron Ion Collider in China: An Impact study on $\text{Im}\mathcal{E}$
• Gross-Llewellyn Smith sum rule from lattice QCD
• Lattice QCD calculation of the Compton amplitude subtraction function
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• Form factors of the $\rho$ meson from effective field theory and the lattice