Threshold effects as the origin of $Y(4500)$ observed in $e^+e^-\to J/ψK^+K^-$

TL;DR

This work addresses the origin of the BESIII observed $Y(4500)$ in $e^{+}e^{-}\to J/\psi K^{+}K^{-}$ by modeling the process with intermediate charmonia and charmed-meson loops within HQSS/HHChPT, and by introducing the hypothetical $Z_{cs}^{(\prime)}$ resonance. The main approach combines contact interactions, triangle-loop rescattering, and a TS mechanism to generate a peak near $\sqrt{s}=4.5$ GeV, examining both a pure $\psi(4415)$ and various $S$-$D$ mixings. The key finding is that the observed peak can be reproduced as a threshold effect arising from TS in the $Z_{cs}^{(\prime)}$-mediated rescattering, rather than from a conventional resonance, with the peak’s presence and strength strongly dependent on the $Z_{cs}^{(\prime)}$ mass and width and on the composition of $\psi(4415)$. Overall, the results support a TS-driven interpretation of $Y(4500)$ and highlight the need for further data to validate the role of near-threshold dynamics and possible related states.

Abstract

The BESIII collaboration has recently observed a resonant structure $Y(4500)$ in $e^{+}e^{-}\to J/ψK^{+}K^{-}$, whose origin remains unresolved. In this study, we analyze the cross section line shape of $e^{+}e^{-}\to J/ψK^{+}K^{-}$ by taking into account the $ψ(4415)$ state and intermediate charmed meson loops. By treating $ψ(4415)$ as both a pure $S$-wave state and $S$-$D$ mixed states, and introducing the $Z_{cs}^{(\prime)}$ resonance, we find that the $Y(4500)$ peak at $\sqrt{s}=4.5~\text{GeV}$ arises from the triangle singularity mechanism in the $Z_{cs}^{(\prime)}$-mediated rescattering processes, supporting its interpretation as a threshold effect rather than a conventional resonance.

Figures (8)

• Figure 1: Feynmann diagrams for $e^{+}e^{-}\to J/\psi K^{+}K^{-}$ via the intermediate charmonium state $\psi(nS/nD)$ and charmed-meson loops. The charge conjugate diagrams are implicit.
• Figure 2: Diagrammatic representation of the rescattering channel via the state $Z_{cs}^{(\prime)}$, showing the subprocess $HH \to J/\psi K$.
• Figure 3: Cross section for $e^{+}e^{-}\to J/\psi K^{+}K^{-}$ as a function of center-of-mass energy. The solid curve represents the calculation with only the contact term included, while the dashed curve includes the $Z_{cs}^{(\prime)}$ propagator. Vertical dashed lines indicate the thresholds for $D_{s0}^* D_s^*$, $D_{s1}^\prime D_s$, and $D_{s1}^\prime D_s^*$ combinations. The shaded region represents uncertainties arising from variations in the mass and width of $Z_{cs}^{(\prime)}$.
• Figure 4: Dependence of the $e^{+}e^{-}\to J/\psi K^{+}K^{-}$ cross section on the mass of $Z_{cs}^{(\prime)}$, with $\delta\equiv M_{Z_{cs}^{(\prime)}}-m_{D^*}-m_{D_s^{(*)}}$ and the width fixed at $\Gamma_{Z_{cs}^{(\prime)}} = 14$ MeV. The curves demonstrate how variations in the $Z_{cs}^{(\prime)}$ mass affect the peak structure around 4.5 GeV.
• Figure 5: Dependence of the $e^{+}e^{-}\to J/\psi K^{+}K^{-}$ cross section on the width of $Z_{cs}^{(\prime)}$, with the mass fixed at $M_{Z_{cs}} = 3988$ MeV and $M_{Z_{cs}^{\prime}} = 4131$ MeV. The suppression of the 4.5 GeV peak with increasing width is clearly visible.