Wave-Packet Effects: A Solution for Isospin Anomalies in Vector-Meson Decay

Abstract

There is a long-standing anomaly in the ratio of the decay width for $\psi(3770)\to D^0\overline{D^0}$ to that for $\psi(3770)\to D^+D^-$ at the level of $9.5\,\sigma$. A similar anomaly exists for the ratio of $\phi(1020)\to K_\text{L}^0K_\text{S}^0$ to $\phi(1020)\to K^+K^-$ at $2.1\,\sigma$. In this study, we reassess the anomaly through the lens of Gaussian wave-packet formalism. Our comprehensive calculations include the localization of the overlap of the wave packets near the mass thresholds as well as the composite nature of the initial-state vector mesons. The results align within $\sim 1 \sigma$ confidence level with the Particle Data Group's central values for a physically reasonable value of the form-factor parameter, indicating a resolution to these anomalies. We also check the deviation of a wave-packet resonance from the Briet-Wigner shape and find that wide ranges of the wave-packet size are consistent with the experimental data.