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

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 generalised 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 Q̄²≈ 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.