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

We report a study of $B\to J\mathrm{/}\psi ({\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-})K$ decays, where $\mathrm{\ell }$ represents an electron or a muon, using $e^{+}{e}^{-}$ collisions at the $\mathrm{{\rm Y}}(4S)$ 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 $B^{+}\to J\mathrm{/}\psi (e^{+}{e}^{-})K^{+}$, $B^{+}\to J\mathrm{/}\psi ({\mu }^{+}{\mu }^{-})K^{+}$, $B^0\to J\mathrm{/}\psi (e^{+}{e}^{-})K_S^0$, and $B^0\to J\mathrm{/}\psi ({\mu }^{+}{\mu }^{-})K_S^0$; the lepton-flavor-dependent isospin asymmetries for the electron [$A_I(B\to J\mathrm{/}\psi (e^{+}{e}^{-})K)$] and muon [$A_I(B\to J\mathrm{/}\psi ({\mu }^{+}{\mu }^{-})K)$] channels; and the ratios of branching fractions between the muon and electron channels for the charged [$R_{K^{+}}\left(J\mathrm{/}\psi \right)$] and neutral kaon [$R_{K^0}\left(J\mathrm{/}\psi \right)$] case. The measurements are consistent with the world-average values.