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

Abstract

AbstractThere is a long-standing anomaly in the ratio of the decay width for $$\psi (3770)\rightarrow D^0\overline{D^0}$$ ψ ( 3770 ) → D 0 D 0 ¯ to that for $$\psi (3770)\rightarrow D^+D^-$$ ψ ( 3770 ) → D + D - at the level of $$9.5\,\sigma $$ 9.5 σ . A similar anomaly exists for the ratio of $$\phi (1020)\rightarrow K_\text {L}^0K_\text {S}^0$$ ϕ ( 1020 ) → K L 0 K S 0 to $$\phi (1020)\rightarrow K^+K^-$$ ϕ ( 1020 ) → K + K - at $$2.1\,\sigma $$ 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 $$\sim 1 \sigma $$ ∼ 1 σ 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.