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

TL;DR

This paper uses lattice QCD to determine off-forward Compton amplitude structure functions, enabling the reconstruction of generalized parton distributions and testing methods for real-time scattering amplitudes with promising phenomenological agreement.

Contribution

It introduces a lattice QCD approach to extract GPDs from off-forward Compton amplitudes and compares different reconstruction methods.

Findings

Good agreement with phenomenology and previous lattice results.

Identification of systematics in GPD reconstruction methods.

Validation of the Feynman-Hellmann approach for structure function determination.

Abstract

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.