Moscow International School of Physics 2020

The ongoing improvement of data of processes such as $B \rightarrow J/\psi ~ \text{K} ~ \pi$ containing $\text{K}\pi$ final state interactions, measured by LHCb or COMPASS, require a theoretically sound description consistent with unitarity and analyticity. The understanding of such meson-meson strong interactions is still unclear and controversial in some energy regions. In particular a lot of resonances are very broad or difficult to distinguish from background. Hence a parametrisation using standard Breit-Wigner resonances is inept. In contrast the N/D-method gives the right branch cut structure consistent with unitarity and analyticity relying on $\chi$PT and resonance exchanges consistent with chiral symmetry.
We want to present our ongoing process of expanding the area of validity for the description of $\text{K}\pi\rightarrow\text{K}\pi$ scattering amplitudes beyond 1.4 GeV using the N/D-method (as done up to 1.4 GeV [1]). The present model is enhanced by taking additionally to the $\text{K}\eta$ coupled channel the $\text{K}\eta^\prime$ into account as well as adding higher energetic resonances. Our main focus will be on $I(J^P)=\frac{1}{2}(0^+)$ s-wave amplitudes, where the $\text{K}^*_0 (700)$ (prior $\kappa$) as well as $\text{K}^*_0 (1430)$ and $\text{K}^*_0 (1950)$ are present. In the future the framework should be expanded to incorporate higher partial waves as well.

[1] J. A. Oller and E. Oset, "N/D description of two meson amplitudes and chiral
symmetry" in Phys. Rev. D60, 1999