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 ${\mathcal{H}}_1$ and ${\mathcal{E}}_1$ 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 $m_{\pi }=412\text{MeV}$ and four values of the soft momentum transfer, $t\approx 0,-0.3,-0.6,-1.1{\text{GeV}}^2$, all at a hard momentum scale of ${\bar{Q}}^2\approx 5{\text{GeV}}^2$. 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.