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On the scalar $\pi K$ form factor beyond the elastic region

by Frederic Noël, Leon von Detten, Christoph Hanhart, Martin Hoferichter, Bastian Kubis

Submission summary

Abstract

Pion--kaon ($\pi K$) final states, often appearing in heavy-particle decays at the precision frontier, are important for Standard-Model tests, to describe crossed channels with exotic states, and for spectroscopy of excited kaon resonances. We construct a representation of the $\pi K$ $S$-wave form factor using the elastic $\pi K$ scattering phase shift via dispersion relations in the elastic region and extend this model into the inelastic region using resonance exchange, while maintaining unitarity and the correct analytic structure. As a first application, we successfully described the $\tau \to K_S \pi \nu_\tau$ spectrum to not only achieve a better distinction between $S$- and $P$-wave contributions, but also to provide an improved estimate of the $CP$ asymmetry produced by a tensor operator as well as the forward--backward asymmetry, both of which can be confronted with future data at Belle II. The work presented here is published in Ref. [1].