Measurement of the branching fractions of $Btoeta K$ decays using 2019/2020 Belle II data

This note describes the rediscovery of $Btoeta K$ decays in Belle II data, both in the charged and neutral final state: $B_0toeta K_S$ and $B^pmtoeta K^pm$. The $eta$ is searched for in two decay modes: $etatoetapi^+pi^-$ with $etatogammagamma$, and $etatorhogamma$. The analysis uses data collected in 2019 and 2020 at the SuperKEKB asymmetric $e^+e^-$ collider, with an integrated luminosity of $62.8~fb^{-1}$, corresponding to $68.2$ million of $Bbar{B}$ pairs produced. The signal yield is obtained via an unbinned maximum likelihood fit to signal sensitive variables, obtaining branching ratios: $$mathcal{B}left(B^pmtoetaK^pmright) = left(63.4~^{+3.4}_{-3.3},(stat),pm3.2,(syst),right) times10^{-6} $$ $$mathcal{B}left(B_0toetaK_Sright) = left(59.9~^{+5.8}_{-5.5},(stat),pm2.9,(syst),right) times10^{-6} $$ which are consistent with world average.