Measurements of the branching fraction, isospin asymmetry, and lepton-universality ratio in $B\to J/\ddot{I}ˆK$ decays at Belle II

Abstract

We report a study of $B\to J/\ddot{I}ˆ({\ell }^{+}{\ell }^{-})K$ decays, where $\ell$ represents an electron or a muon, using $e^{+}{e}^{-}$ collisions at the $\hat{I}\yen (4S)$ resonance. The data were collected by the Belle II experiment at the SuperKEKB asymmetric-energy collider during 2019-2021, corresponding to an integrated luminosity of $189$ fb${}^{-1}$. The measured quantities are the branching fractions ($\mathcal{B}$) of the decay channels $B^{+}\to J/\ddot{I}ˆ(e^{+}{e}^{-})K^{+}$, $B^{+}\to J/\ddot{I}ˆ(\hat{I}{¼}^{+}\hat{I}{¼}^{-})K^{+}$, $B^0\to J/\ddot{I}ˆ(e^{+}{e}^{-})K_S^0$, and $B^0\to J/\ddot{I}ˆ(\hat{I}{¼}^{+}\hat{I}{¼}^{-})K_S^0$; the lepton-flavor-dependent isospin asymmetries for the electron [$A_I\left(B\to J/\ddot{I}ˆ(e^{+}{e}^{-})K\right)$] and muon [$A_I\left(B\to J/\ddot{I}ˆ(\hat{I}{¼}^{+}\hat{I}{¼}^{-})K\right)$] channels; and the ratios of branching fractions between the muon and electron channels for the charged [$R_{K^{+}}\left(J/\ddot{I}ˆ\right)$] and neutral kaon [$R_{K^0}\left(J/\ddot{I}ˆ\right)$] case. The measurements are consistent with the world-average values.