Generalized parton distributions from the off-forward Compton amplitude in lattice QCD
A. Hannaford-Gunn, Kadir Utku Can, R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, H. Stüben, R. D. Young, J. M. Zanotti
Abstract
We determine the properties of generalized 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 parametrized 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, $t=\ensuremath{-}1.1,\ensuremath{-}2.2\text{ }\text{ }{\mathrm{GeV}}^{2}$, and a pion mass of ${m}_{\ensuremath{\pi}}\ensuremath{\approx}470\text{ }\text{ }\mathrm{MeV}$. 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.