Decoding the structure near the $π^+π^-$ mass threshold in $ψ(3686) \rightarrow J/ψπ^+π^-$ decays

TL;DR

The paper addresses the near-threshold structure seen in the dipion transition ψ'→J/ψππ by employing a model-independent dispersion-theory treatment of ππ final-state interactions. It combines chiral contact terms with a left-hand-cut Z_c(3900) exchange and Omnès unitarization to describe the ππ system, and fits to BESIII data on the ππ mass spectrum and helicity distributions. The analysis shows that the observed threshold feature can be reproduced without introducing a new resonance, while the virtual Z_c exchange further improves agreement, especially in the low-energy region and angular observables; helicity-flip amplitudes play a significant role in shaping the spectrum. Overall, the work clarifies the impact of ππ FSI and isovector exotic exchanges in heavy-quarkonium transitions using a robust, model-independent framework for final-state interactions.

Abstract

In light of recent high-precision data taken by the BESIII Collaboration, we reconsider the dipion transition $ψ(3686) \rightarrow J/ψπ^+π^-$. The strong pion-pion final-state interactions are taken into account model-independently by using dispersion theory. We find that we can reproduce the substructure near the $π^+π^-$ threshold observed experimentally without introducing an extra resonance state. While a helicity-flip amplitude plays an important role for the formation of the dip in the invariant-mass distribution, virtual exchange of the charmoniumlike exotic $Z_c(3900)$ state improves the fit quality significantly.

Figures (4)

• Figure 1: Diagrams considered for $\psi' \rightarrow J/\psi \pi^+\pi^-$. Diagram (a) denotes the contributions of the chiral contact terms, while diagram (b) corresponds to the contributions of the $Z_c$ exchange. The gray blob denotes pion--pion rescattering.
• Figure 2: Fit results of the $\pi\pi$ invariant-mass spectra (top) and the $\cos\theta$ distributions (bottom) in $\psi' \to J/\psi \pi\pi$ of Fits I (blue dotted), II (red solid), and III (green dashed). The zoomed inset (top) shows the fit results in the region of $(0.28, 0.32)$ GeV. In the $\cos\theta$ distributions (bottom), the zero is suppressed to make differences in the fits visible. The data are taken from Ref. BESIII:2025ozb.
• Figure 3: Fit results of the folded $\pi\pi$ spectra data without efficiency correction in the range of $M(\pi^+\pi^-) \in (0.28, 0.32)$ GeV in $\psi' \to J/\psi \pi\pi$ of Fits Ib (blue dotted), IIb (red solid), and IIIb (green dashed).
• Figure 4: The moduli of the $S$- (left) and $D$-wave (right) amplitudes for $\psi' \to J/\psi \pi^+\pi^-$ in Fits I (top) and II (bottom). The red solid lines represent our best fit results, while the blue dotted, orange dashed, dark green dot-dashed, and thick black solid lines correspond to the contributions from the chiral contact terms proportional to $g_1$, $h_1$, and $j_1$, as well as the $Z_c$-exchange term, respectively.