Measurements of the branching fractions for $B \to K^{*}��$ decays at Belle II

This paper reports a study of $B \to K^{*}��$ decays using $62.8\pm 0.6$ fb$^{-1}$ of data collected during 2019--2020 by the Belle II experiment at the SuperKEKB $e^{+}e^{-}$ asymmetric-energy collider, corresponding to $(68.2 \pm 0.8) \times 10^6$ $B\overline{B}$ events. We find $454 \pm 28$, $50 \pm 10$, $169 \pm 18$, and $160 \pm 17$ signal events in the decay modes $B^{0} \to K^{*0}[K^{+}��^{-}]��$, $B^{0} \to K^{*0}[K^0_{\rm S}��^{0}]��$, $B^{+} \to K^{*+}[K^{+}��^{0}]��$, and $B^{+} \to K^{*+}[K^{+}��^{0}]��$, respectively. The uncertainties quoted for the signal yield are statistical only. We report the branching fractions of these decays: $$\mathcal{B} [B^{0} \to K^{*0}[K^{+}��^{-}]��] = (4.5 \pm 0.3 \pm 0.2) \times 10^{-5}, $$ $$\mathcal{B} [B^{0} \to K^{*0}[K^0_{\rm S}��^{0}]��] = (4.4 \pm 0.9 \pm 0.6) \times 10^{-5},$$ $$\mathcal{B} [B^{+} \to K^{*+}[K^{+}��^{0}]��] = (5.0 \pm 0.5 \pm 0.4)\times 10^{-5},\text{ and}$$ $$\mathcal{B} [B^{+} \to K^{*+}[K^0_{\rm S}��^{+}]��] = (5.4 \pm 0.6 \pm 0.4) \times 10^{-5},$$ where the first uncertainty is statistical, and the second is systematic. The results are consistent with world-average values.