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Pion-kaon ($\pi K$) pairs occur frequently as final states in heavy-particle decays.

A consistent treatment of $\pi K$ 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 $\pi K$ scattering in a given partial wave are related to the phases of the respective $\pi K$ form factors by Watson's theorem.

Going beyond that, we constructed in Ref.[1] a representation of the scalar $\pi K$ form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $\pi K$ scattering and maintaining the correct analytic structure.

As a first application, we considered the decay ${\tau\to K_S\pi\nu_\tau}$, in particular, we studied to which extent the $S$-wave $K_0^*(1430)$ and the $P$-wave $K^*(1410)$ resonances can be differentiated and provide an improved estimate of the $CP$ asymmetry produced by a tensor operator.

[1] Von Detten, L. and Noël, F. and Hanhart, C. and Hoferichter, M. and Kubis, B.

Eur. Phys. J. C 81, 420 (2021); DOI: 10.1140/epjc/s10052-021-09169-7

What is your topic? | Hadronic decays |
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