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

There is a long-standing anomaly in the ratio of the decay width for ψ(3770) → D${}^0\overline{D^0}$ to that for ψ(3770) → D${}^{+}$D${}^{-}$ at the level of 9.5 σ. A similar anomaly exists for the ratio of ϕ(1020) → K${}_L^0$K${}_S^0$ to ϕ(1020) → K${}^{+}$K${}^{-}$ at 2.1 σ. 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 ∼ 1σ. 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.