Combined analysis of the decays $\ddot{I}{„}^{-}\to K_S\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ and $\ddot{I}{„}^{-}\to K^{-}\hat{I}\cdot \hat{I}{½}_{\ddot{I}}„$

Abstract

In a combined study of the decay spectra of $\ddot{I}{„}^{-}\to K_S\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ and $\ddot{I}{„}^{-}\to K^{-}\hat{I}\cdot \hat{I}{½}_{\ddot{I}}„$ decays within a dispersive representation of the required form factors, we illustrate how the $K^{\ast }(1410)$ resonance parameters, defined through the pole position in the complex plane, can be extracted with improved precision as compared to previous studies. While we obtain a substantial improvement in the mass, the uncertainty in the width is only slightly reduced, with the findings $M_{K^{\ast \prime }}=1304\pm 17$MeV and $\hat{I}{“}_{K^{\ast \prime }}=171\pm 62$MeV. Further constraints on the width could result from updated analyses of the $K\ddot{I}€$ and/or $K\hat{I}\cdot$ spectra using the full Belle-I data sample. Prospects for Belle-II are also discussed. As the $K^{-}\ddot{I}{€}^0$ vector form factor enters the description of the decay $\ddot{I}{„}^{-}\to K^{-}\hat{I}\cdot \hat{I}{½}_{\ddot{I}}„$, we are in a position to investigate isospin violations in its parameters like the form factor slopes. In this respect also making available the spectrum of the transition $\ddot{I}{„}^{-}\to K^{-}\ddot{I}{€}^0\hat{I}{½}_{\ddot{I}}„$ would be extremely useful, as it would allow to study those isospin violations with much higher precision.

20 pages, 1figure