Observation of $\psi \mathbf{(}4040\mathbf{)}$ and $\psi \mathbf{(}4160\mathbf{)}$ decay into $\eta J/\psi$

The cross section for $e^{+}{e}^{-}\to \eta J/\psi$ between $\sqrt{s}=3.8\mathrm{GeV}$ and 5.3 GeV is measured via initial state radiation using $980{\mathrm{fb}}^{-1}$ of data on and around the ${\rm Y}(nS)(n=1,2,3,4,5)$ resonances collected with the Belle detector at KEKB. Two resonant structures at the $\psi (4040)$ and $\psi (4160)$ are observed in the $\eta J/\psi$ invariant mass distribution. Fitting the mass spectrum with the coherent sum of two Breit-Wigner functions, one obtains $\mathcal{B}(\psi (4040)\to \eta J/\psi )·{\Gamma }_{e^{+}{e}^{-}}^{\psi (4040)}=(4.8\pm 0.9\pm 1.5)\mathrm{eV}$ and $\mathcal{B}(\psi (4160)\to \eta J/\psi )·{\Gamma }_{e^{+}{e}^{-}}^{\psi (4160)}=(4.0\pm 0.8\pm 1.4)\mathrm{eV}$ for one solution and $\mathcal{B}(\psi (4040)\to \eta J/\psi )·{\Gamma }_{e^{+}{e}^{-}}^{\psi (4040)}=(11.2\pm 1.3\pm 2.1)\mathrm{eV}$ and $\mathcal{B}(\psi (4160)\to \eta J/\psi )·{\Gamma }_{e^{+}{e}^{-}}^{\psi (4160)}=(13.8\pm 1.3\pm 2.1)\mathrm{eV}$ for the other solution, where the first errors are statistical and the second are systematic. This is the first measurement of this hadronic transition mode of these two states, and the partial widths to $\eta J/\psi$ are found to be about 1 MeV. There is no evidence for the $Y(4260)$, $Y(4360)$, $\psi (4415)$, or $Y(4660)$ in the $\eta J/\psi$ final state, and upper limits of their production rates in $e^{+}{e}^{-}$ annihilation are determined.

Figure 1

Invariant mass distributions of (a) ${\ell }^{+}{\ell }^{-}$ vs ${\pi }^{+}{\pi }^{-}{\pi }^0$ and (b) ${\ell }^{+}{\ell }^{-}$ vs $\gamma \gamma$ for selected ${\pi }^{+}{\pi }^{-}{\pi }^0{\ell }^{+}{\ell }^{-}$ or $\gamma \gamma {\ell }^{+}{\ell }^{-}$ candidates with invariant mass between $3.8\mathrm{GeV}/c^2$ and $5.3\mathrm{GeV}/c^2$. The box in the center of each plot shows the $\eta J/\psi$ signal region while the surrounding boxes show the sideband regions.

Figure 2

The invariant mass distribution of the $\eta J/\psi$ candidates. The top row shows the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ mode and the bottom row shows the $\eta \to \gamma \gamma$ mode. The open histograms are from the $\eta$ and $J/\psi$ signal region, while the shaded ones are from their sideband regions after the proper normalization. The insets show the distributions around the $\psi (2S)$ mass region.

Figure 3

The $\eta J/\psi$ invariant mass distribution and the fit results. The points with error bars show the data while the shaded histogram is the normalized $\eta$ and $J/\psi$ background from the sidebands. The curves show the best fit on signal candidate events and sideband events simultaneously (solid red line) and the contribution from each Breit-Wigner component (pink dashed and black dotted for the two solutions discussed in the text). Note that the interference term (not shown) for each solution is substantial.

Figure 4

The measured $e^{+}{e}^{-}\to \eta J/\psi$ cross section for $\sqrt{s}=3.8\mathrm{GeV}$ to 5.3 GeV. The errors are the summed statistical errors of the numbers of signal and background events. A systematic error of 8.0% common to all the data points is not shown.