Data taking strategy for $\psi(3770)$ and $\Upsilon(4S)$ branching fraction measurements at $e^+e^-$ colliders

TL;DR

This paper develops an optimized data collection strategy for measuring rare decay modes of heavy quarkonium states at electron-positron colliders, using simulations and information theory to identify ideal energy points.

Contribution

It introduces a systematic approach combining Monte Carlo simulations and Fisher information to determine optimal energy points for precise branching fraction measurements.

Findings

Optimal energy points identified for $ ext{psi}(3770)$ and $ ext{Upsilon}(4S)$ decays.

Methodology improves measurement precision for rare decay channels.

Analysis of how luminosity affects measurement accuracy.

Abstract

The $\psi(3770)$ and $\Upsilon(4S)$ states predominantly decay into open-flavor meson pairs, whereas 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 $\psi(3770) \to \mbox{\text{non}-}D\bar{D}$ 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 $3.769~\gev$ and $3.781~\gev$, whereas those for $\Upsilon(4S) \to \mbox{\text{non}-}B\bar{B}$ decays are $10.574~\gev$ and $10.585~\gev$. 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.