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

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 GeV${}^2$, and a pion mass of m${}_{\pi }$ ≈ 470 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.