Search for the reaction channel $e^+ e^- \to ηη\,J/ψ$ and the isospin partner of the $Z_c(3900)$ at center-of-mass energies $\sqrt{s} = 4.226-4.950$ GeV

TL;DR

The study conducts a comprehensive search for e+e− → ηη J/ψ in BESIII data spanning √s = 4.226–4.950 GeV, employing two complementary approaches: an exclusive method reconstructing all final-state particles and a semi-inclusive method with one η observed and the other inferred. While the exclusive channel yields 8.9σ at 4.750 GeV and 5.7σ at 4.682 GeV, most energies show no significant signal, prompting 90% CL upper limits on the Born cross section; the semi-inclusive method finds evidence at several energies but with smaller significance and larger uncertainties. The combined results reveal marked deviations from pure three-body phase space around 4.4 GeV but do not provide conclusive evidence for a Zc isospin partner decaying to J/ψη. The findings place stringent constraints on ηη J/ψ production and related Zc-like states, underscoring the need for larger data samples to clarify potential resonant contributions. Together, these analyses constrain exotic-state interpretations in this final state and guide future searches in the charmonium-like sector.

Abstract

We search for the reaction channel $e^+ e^- \to ηη\,J/ψ$ in a data sample with center-of-mass energies from 4.226 to 4.950~GeV, which was collected by the BESIII detector operating at the Beijing Electron Positron Collider (BEPCII). The data analysis is performed with two different methods, exclusively and semi-inclusively, which enabling a comparison and combination of the results. Only in a few cases a statistical significance of the cross sections with more than $3σ$ is observed with one of the methods. Only at 4.750~GeV the significance of the cross section measurement is 8.9$σ$ (observation) with the exclusive analysis and 3.4$σ$ (evidence) with the semi-inclusive analysis. Therefore, the corresponding upper limits of the cross section at the 90% confidence level are determined. The energy dependent results show clear deviations from the the line shape expected from three-body phase space alone. Since the statistical significance for almost all center-of-mass energies is low, the upper limits for the reaction channel $e^+ e^- \to ηη\,J/ψ$ also serve as limits for the existence of a possible isospin partner to the charmonium-like isospin triplet $Z_{\rm c}(3900)$ which decays to $J/ψη$.

Figures (10)

• Figure 1: Invariant mass distributions for (a) $J/\psi \to l^+l^-$ and (b) $\eta \to \gamma\gamma$ candidates at $\sqrt{s} = 4.42GeV$. Black dots with error bars represent data (the number of $\eta$ candidates is twice the number of $J/\psi$ candidates), red histograms the signal MC sample, and the green area the background MC sample. The scaling of the MC sample is arbitrary.
• Figure 2: Two-dimensional efficiency distributions as a function of the squared invariant mass $M^2(\eta\eta)$ and $M^2(J/\psi \eta)$ at $\sqrt{s} = 4.42\GeV$ for (a) $\epsilon_{\rm 11}$ with $\eta\eta \to 4\gamma$, (b) $\epsilon_{\rm 12}$ with $\eta\eta \to 2\gamma\,\pi^{+}\pi^{-}\pi^{0}$ and (c) $\epsilon_{\rm 22}$ with $\eta\eta \to 2\left(\pi^{+}\pi^{-}\pi^{0}\right)$.
• Figure 3: Distributions of (a) $M(J/\psi\eta)$ (two entries per event) and (b) $M(\eta\eta)$ (one entry) summed over all energies.
• Figure 4: ISR correction for the reaction channel $e^{+} e^{-} \to \eta \eta J/\psi$, $\eta\eta \to 4\gamma$, at $\sqrt{s}= 4.36\MeV$. (a) Normalized reconstruction efficiency versus $E_{\rm ISR}/E_{\rm beam}$, where the red curve represents the fit with the error function; (b) dependence of the ISR correction factor $(1+\delta)$ on $\sqrt{s}$, assuming a single narrow resonance with mass of 4.26 GeV/$c^{2}$ and width of $10\MeV$.
• Figure 5: Observed cross sections (green) and upper limits (blue) at the 90% CL on the Born cross section as a function of the CM energy. For the observed cross section, only the statistical uncertainties are shown as error bars.