Measurement of the branching fraction for $psi(3686)toomega K^+ K^-$

With $1.06times 10^8$ $psi(3686)$ events collected with the BESIII detector, the branching fraction of $psi(3686) to omega K^+ K^-$ is measured to be $(1.54 pm 0.04 pm 0.11) times 10^{-4}$. This is the most precise result to date, due to the largest $psi(3686)$ sample, improved signal reconstruction efficiency, good simulation of the detector performance, and a more accurate knowledge of the continuum contribution. Using the branching fraction of $J/psi to omega K^+ K^-$, the ratio $mathcal{B}(psi(3868) to K^+K^-) / mathcal{B}(J/psi to K^+K^-)$ is determined to be $(18.4 pm 3.7),%$. This constitutes a significantly improved test of the $12,%$ rule, with the uncertainty now dominated by the $J/psi$ branching fraction.