Combined analysis of Belle and Belle II data to determine the CKM angle $\ddot{I}{•}_3$ using $B^{+}\to D(K_S^0{h}^{-}{h}^{+})h^{+}$ decays

Abstract

We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle $\ddot{I}{•}_3$ (also known as~${\hat{I}}^3$) using a model-independent Dalitz plot analysis of \linebreak $B^{+}\to D\left(K_S^0{h}^{+}{h}^{-}\right)h^{+}$, where $D$ is either a $D^0$ or $\bar{D}{}^0$ meson and $h$ is either a $\ddot{I}€$ or $K$. This is the first measurement that simultaneously uses Belle and Belle~II data, combining samples corresponding to integrated luminosities of \SI{711}{fb^{-1}} and \SI{128}{fb^{-1}}, respectively. All data were accumulated from energy-asymmetric $e^{+}{e}^{-}$ collisions at a centre-of-mass energy corresponding to the mass of the $\hat{I}\yen (4S)$ resonance. We measure $\ddot{I}{•}_3={\left(78.4\pm 11.4\pm 0.5\pm 1.0\right)}^{\circ }$, where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is from the uncertainties on external measurements of the $D$-decay strong-phase parameters.

34 pages, 11 figures