On the scalar form factor beyond the elastic region

Pion-kaon ( $$ ) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $$ 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 $$ scattering in a given partial wave are related to the phases of the respective $$ form factors by Watson's theorem. Going beyond that, we here construct a representation of the scalar $$ form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $$ scattering and maintaining the correct analytic structure. As a first application, we consider the decay $$ , in particular, we study to which extent the S-wave $$ and the P-wave $$ resonances can be differentiated and provide an improved estimate of the CP asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the $$ and $$ resonances via Padé approximants, $$ and $$ , as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for $$ in terms of the corresponding residue, leading to the upper limit $$ .