https://doi.org/10.1140/epjc/s10052-021-09169-7
Regular Article - Theoretical Physics
On the scalar 
form factor beyond the elastic region
1
Forschungszentrum Jülich, Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, 52425, Jülich, Germany
2
Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
3
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany
Received:
4
March
2021
Accepted:
19
April
2021
Published online:
14
May
2021
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 
.
© The Author(s) 2021
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Funded by SCOAP3
