Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness

Abstract: We extend the formalism of asymmetric frames of reference for generalized parton distributions (GPDs) to the case of nonzero skewness, i.e., including longitudinal momentum transfer. The framework, based on Lorentz-invariant amplitudes and previously developed and numerically implemented for unpolarized, helicity and transversity GPDs at zero skewness, gives efficient access to a broad range of kinematics, making full mapping of GPDs from the lattice realistic. The general-skewness formalism is tested using lattice data with both transverse and longitudinal or only longitudinal momentum transfer, the latter being a special case with a reduced number of independent amplitudes. We extract the amplitudes in coordinate space and express the GPDs $H$ and $E$ in terms of these amplitudes. This is followed by reconstruction of quasi-distributions and their matching to the light cone. We further identify and discuss the principal challenges for nonzero skewness GPDs.