Revealing di-pion correlations for the observed substructure near the $π^+π^-$ mass threshold in $ψ(3686)\to J/ψπ^+π^-$

Abstract

Based on the world's largest $ψ(3686)$ data sample, the BESIII Collaboration recently reported a substructure near the $π^+π^-$ mass threshold in the decay $ψ(3686) \to J/ψπ^+π^-$, challenging the established understanding of the di-pion invariant mass spectrum. We propose that this substructure arises directly from di-pion correlations. Using a chiral unitary approach, we successfully reproduce the observed anomaly, thereby providing strong evidence of di-pion correlation in heavy quarkonium decays. This approach also allows us to predict the corresponding di-pion correlation function.

Figures (5)

• Figure 1: Topological diagrams corresponding to the (a) $(M)_{44} \text{Tr}(M \cdot M)$ and (b) $(M)_{44} \text{Tr}(M) \text{Tr}(M)$ terms.
• Figure 2: Diagrams contributing to $\psi(3686) \to J/\psi\pi^+\pi^-$.
• Figure 3: (a) $\pi^{+}\pi^{-}$ invariant mass distribution near threshold in $\psi(3686) \rightarrow J/\psi\pi^{+}\pi^{-}$ compared with experimental data BESIII:2025ozb. (b) Contributions from the two mechanisms in Fig. \ref{['fig:Feynman1']}. (c) $J/\psi\pi^{+}$ invariant mass spectrum.
• Figure 4: Full $\pi^{+}\pi^{-}$ invariant mass distribution in $\psi(3686) \rightarrow J/\psi\pi^{+}\pi^{-}$. Data points are from BESIII BESIII:2025ozb.
• Figure 5: Source size dependence of the correlation functions with the Gaussian source for $\pi^{+}\pi^{-}$ (a) and $\pi^{0}\pi^{0}$ (b) in coupled channels, taking $q_{max} = 0.6~ \rm GeV$. The results obtained with source sizes $R = 0.7$, $1.0$, $1.6$, and $3.0$ fm are denoted by the red solid line, the blue dashed line, the green dash-dotted line, and the black dotted line, respectively.