Eur. Phys. J. C (2023) 83: 978
https://doi.org/10.1140/epjc/s10052-023-12077-7

Regular Article - Theoretical Physics

Wave-packet effects: a solution for isospin anomalies in vector-meson decay

¹ Department of Physics, Faculty of Science, Hokkaido University, 060-0810, Sapporo, Japan
² Natural Science Center, Keio University, 223-8521, Yokohama, Japan
³ Department of Physics, Faculty of Science, Tokyo Institute of Technology, 152-8550, Tokyo, Japan
⁴ Department of Physics, Shiv Nadar Institution of Eminence, 201314, Gautam Buddha Nagar, India
⁵ Department of Mathematics, Tokyo Woman’s Christian University, 167-8585, Tokyo, Japan

^c kenji.nishiwaki@snu.edu.in

Received: 28 August 2023
Accepted: 24 September 2023
Published online: 30 October 2023

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 $\varphi (1020)\to K_{\text{L}}^0{K}_{\text{S}}^0$ to $\varphi (1020)\to K^{+}{K}^{-}$ at $2.1\sigma$. In this study, we reassess the anomaly through the lens of a Gaussian wave-packet formalism. Our comprehensive calculations include the localization of the overlap of the wave packets near the mass thresholds and the composite nature of the initial-state vector mesons. The results align within a $\sim 1\sigma$ 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.