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

We present a determination of the structure functions of the off-forward Compton amplitude H 1 and E 1 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 m π = 412 MeV and four values of the soft momentum transfer, t ≈ 0 , − 0.3 , − 0.6 , − 1.1 GeV 2 , all at a hard momentum scale of Q ¯ 2 ≈ 5 GeV 2 . 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.