On the scalar [Formula: see text] form factor beyond the elastic region

Pion–kaon ([Formula: see text] ) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of [Formula: see text] scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of [Formula: see text] scattering in a given partial wave are related to the phases of the respective [Formula: see text] form factors by Watson’s theorem. Going beyond that, we here construct a representation of the scalar [Formula: see text] form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from [Formula: see text] scattering and maintaining the correct analytic structure. As a first application, we consider the decay [Formula: see text] , in particular, we study to which extent the S-wave [Formula: see text] and the P-wave [Formula: see text] resonances can be differentiated and provide an improved estimate of the CP asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the [Formula: see text] and [Formula: see text] resonances via Padé approximants, [Formula: see text] and [Formula: see text] , as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for [Formula: see text] in terms of the corresponding residue, leading to the upper limit [Formula: see text] .