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### Description

The nucleon forward Compton amplitude describes the process of a virtual photon scattering on a nucleon. It is an important object which encodes insights into hadronic structure. The real part of this amplitude contains a component that is unconstrained by a dispersive representation in terms of inelastic scattering data. This component, commonly referred to as the `subtraction function', contributes significantly to the determination of key physical quantities such as the electromagnetic portion of the proton-neutron mass difference and hence constraining this function has gained renewed interest. Using lattice QCD, the second order Feynman-Hellmann theorem can be utilised to calculate the nucleon forward Compton amplitude. By judiciously choosing the photon and nucleon momenta and direction of the electromagnetic current, the subtraction function $S_1(Q^2)$ can be calculated at fixed photon virtuality, $Q^2$. The subtraction function is calculated for a range of photon momenta up to high $Q^2 \approx 11$ GeV$^2$, using different discretisations of the electromagnetic current. The results indicate an asymptotic behaviour that differs from that anticipated from the operator product expansion. A comparison of results between differing quark masses and lattice volumes and spacings is made to determine whether the behaviour survives the physical limit.