Analytic structure of Compton-like transitions to two-body states

We describe the on-shell representation of transitions from a single-hadron to a two-hadron state mediated by the insertion of two external electroweak currents. We demonstrate how structural information of resonances, which couple to the two-body state, can be extracted from the analytic continuation of these amplitudes. Similarly, reactions of this form are of interest within precision studies of the Standard Model like rare kaon decays or the hadronic contribution to the muon anomalous magnetic moment. To date, most of the theoretical descriptions of these amplitudes are data-driven or rely on low energy effective theories. However, the possibility of calculating them from first-principles has become attainable thanks to the development of techniques utilizing the non-perturbative correlation functions obtained from lattice QCD. Similar to S-matrix elements and hadronic transitions involving a single current, the on-shell representation is needed to constrain these amplitudes from lattice data. We will also outline how the on-shell representation is derived to all-orders in the strong coupling from the self-consistent integral equation describing the amplitude.