Reconstructing generalized parton distributions from the lattice off-forward Compton amplitude

Abstract

We present a determination of the structure functions of the off-forward Compton amplitude H1 and E1 from the Feynman-Hellmann method in lattice QCD. At leading twist, these structure functions give access to the generalized parton distributions (GPDs) H and E, respectively. This calculation is performed for an unphysical pion mass of mπ=412  MeV and four values of the soft momentum transfer, t≈0,−0.3,−0.6,−1.1  GeV2, all at a hard momentum scale of Q¯2≈5  GeV2. Using these results, we test various methods to determine properties of the real-time scattering amplitudes and GPDs: (1) we fit their Mellin moments, and (2) we use a simple GPD ansatz to reconstruct the entire distribution. Our final results show promising agreement with phenomenology and other lattice results and highlight specific systematics in need of control. Published by the American Physical Society 2024