Data taking strategy for the phase study in $\psi^{\prime} \to K^+K^-$

TL;DR

This paper investigates the optimal data collection strategy for measuring the phase between strong and electromagnetic decay amplitudes in $\psi^{ ightarrow} K^+K^-$, concluding that a single well-placed data point near the resonance peak suffices for precise measurement.

Contribution

It provides a theoretical analysis and numerical validation showing that one data point near the resonance peak is optimal for phase measurement in $\psi^{ ightarrow} K^+K^-$ decays.

Findings

One data point near the resonance peak is sufficient for phase measurement.

The method extends to estimating resonance mass and decay width.

Numerical simulations validate the optimal data taking strategy.

Abstract

The study of the relative phase between strong and electromagnetic amplitudes is of great importance for understanding the dynamics of charmonium decays. The information of the phase can be obtained model-independently by fitting the scan data of some special decay channels, one of which is $\psi^{\prime} \to K^{+}K^{-}$. To find out the optimal data taking strategy for a scan experiment in the measurement of the phase in $\psi^{\prime} \to K^{+} K^{-}$, the minimization process is analyzed from a theoretical point of view. The result indicates that for one parameter fit, only one data taking point in the vicinity of a resonance peak is sufficient to acquire the optimal precision. Numerical results are obtained by fitting simulated scan data. Besides the results related to the relative phase between strong and electromagnetic amplitudes, the method is extended to analyze the fits of other resonant parameters, such as the mass and the total decay width of $\psi^{\prime}$.