S. Halder ; R. Tiwary ; S. Sandilya ; G. B. Mohanty

21 July 2022

Abstract: We report a study of $B \to J/\psi(\ell^{+}\ell^{-}) K$ decays, where $\ell$ represents an electron or a muon, using $e^{+}e^{-}$ collisions at the $\Upsilon(4S)$ 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 $B^{+} \to J/\psi(e^{+}e^{-}) K^{+}$, $B^{+} \to J/\psi(\mu^{+}\mu^{-}) K^{+}$, $B^{0} \to J/\psi(e^{+}e^{-}) K^{0}_{S}$, and $B^{0} \to J/\psi(\mu^{+}\mu^{-}) K^{0}_{S}$; the lepton-flavor-dependent isospin asymmetries for the electron [$A_{I}\left(B \to J/\psi(e^{+}e^{-}) K\right)$] and muon [$A_{I}\left(B \to J/\psi(\mu^{+} \mu^{-}) K\right)$] channels; and the ratios of branching fractions between the muon and electron channels for the charged [$R_{K^{+}}\left(J/\psi\right)$] and neutral kaon [$R_{K^{0}}\left(J/\psi\right)$] case. We obtain \begin{eqnarray*} \mathcal{B} \left( B^{+} \to J/\psi(e^{+} e^{-}) K^{+}\right) &=& (6.00 \pm 0.10 \pm 0.19) \times 10^{-5},\\ \mathcal{B} \left( B^{+} \to J/\psi(\mu^{+} \mu^{-}) K^{+}\right) &=& (6.06 \pm 0.09 \pm 0.19) \times 10^{-5},\\ \mathcal{B} \left( B^{0} \to J/\psi(e^{+} e^{-}) K_{S}^{0} \right) &=& (2.67 \pm 0.08 \pm 0.12) \times 10^{-5},\\ \mathcal{B} \left( B^{0} \to J/\psi(\mu^{+} \mu^{-}) K_{S}^{0} \right) &=& (2.78 \pm 0.08 \pm 0.12) \times 10^{-5},\\ A_{I} \left( B \to J/\psi(e^{+} e^{-}) K\right) &=& -0.022 \pm 0.016 \pm 0.030,\\ A_{I} \left( B \to J/\psi(\mu^{+} \mu^{-}) K\right) &=& -0.006 \pm 0.015 \pm 0.030,\\ R_{K^{+}}\left(J/\psi\right) &=& 1.009 \pm 0.022 \pm 0.008, \text{ and}\\ R_{K^{0}}\left(J/\psi\right) &=& 1.042 \pm 0.042 \pm 0.008, \end{eqnarray*} where the first uncertainties are statistical and the second are systematic. The measurements are consistent with the world-average values.

Keyword(s): Belle II