Measurement of the $B^+/B^0$ production ratio in $e^+e^-$ collisions at the $\Upsilon(4S)$ resonance using $B \rightarrow J/\psi(\ell\ell) K$ decays at Belle

We measure the ratio of branching fractions for the $\Upsilon (4S)$ decays to $B^+B^-$ and $B^0\bar{B}{}^0$ using $B^+ \rightarrow J/\psi(\ell\ell) K^+$ and $B^0 \rightarrow J/\psi(\ell\ell) K^0$ samples, where $J/\psi(\ell\ell)$ stands for $J/\psi \to \ell^+\ell^-$ ($\ell = e$ or $\mu$), with $711$ fb$^{-1}$ of data collected at the $\Upsilon(4S)$ resonance with the Belle detector. We find the decay rate ratio of $\Upsilon(4S) \rightarrow B^+B^-$ over $\Upsilon(4S) \rightarrow B^0\bar{B}{}^0$ to be $1.065\pm0.012\pm 0.019 \pm 0.047$, which is the most precise measurement to date. The first and second uncertainties are statistical and systematic, respectively, and the third uncertainty is systematic due to the assumption of isospin symmetry in $B \to J/\psi(\ell\ell) K$.