Data taking strategy for ψ(3770) and ϒ(4S) branching fraction measurements at e+e- colliders

Abstract The $\psi(3770)$ and $\Upsilon(4S)$ states predominantly decay into open-flavor meson pairs, while the decays of $\psi(3770) \to \mbox{\text{non}-}D\bar{D}$ and $\Upsilon(4S) \to \mbox{\text{non}-}B\bar{B}$ are rare but crucial for elucidating the inner structure and decay dynamics of heavy quarkonium states. To achieve precise branching fraction measurements for the $\psi(3770) \to \mbox{\text{non}-}D\bar{D}$ and $\Upsilon(4S) \to \mbox{\text{non}-}B\bar{B}$ decays at the high luminosity $e^+e^-$ annihilation experiments, we employed Monte Carlo simulations and Fisher information to evaluate various data taking scenarios, ultimately determining the optimal scheme. The consistent results of both methodologies indicate that the optimal energy points for studies of $\psi(3770) \to \mbox{\text{non}-}D\bar{D}$ decays are $3.769~{\rm GeV}$ and $3.781~{\rm GeV}$, while those for $\Upsilon(4S) \to \mbox{\text{non}-}B\bar{B}$ decays are $10.574~{\rm GeV}$ and $10.585~{\rm GeV}$. In addition, we provide an analysis of the relationship between the integrated luminosity and the precision in branching fraction measurements derived from these data samples, with the branching fraction spanning several orders of magnitude. In addition, we studied the dependence of the precision in branching
fraction measurements on the integrated luminosity, with the branching fractions spanning several
orders of magnitude.