Regular Article - Theoretical Physics
On the scalar form factor beyond the elastic region
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
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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