Abstract
Pion-kaon ( πK ) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of πK 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 πK scattering in a given partial wave are related to the phases of the respective πK form factors by Watson's theorem. Going beyond that, we here construct a representation of the scalar πK form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from πK scattering and maintaining the correct analytic structure. As a first application, we consider the decay τ → KSπντ , in particular, we study to which extent the S-wave K0∗(1430) and the P-wave K∗(1410) 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 K0∗(1430) and K0∗(1950) 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 τ → K0∗(1430)ντ in terms of the corresponding residue, leading to the upper limit BR(τ → K0∗(1430)ντ) < 1.6 × 10-4 .