Updated cross section measurement of $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$ and $K_S^0{K}_S^{0}J/\psi$ via initial state radiation at Belle

The cross sections of the processes $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$ and $K_S^0{K}_S^{0}J/\psi$ are measured via initial state radiation at center-of-mass energies between the threshold and 6.0 GeV using a data sample of $980{\mathrm{fb}}^{-1}$ collected with the Belle detector on or near the $\mathrm{{\rm Y}}(nS)$ resonances, where $n=1,2,\dots ,5$. The cross sections for $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$ are at a few pb level and the average cross section for $e^{+}{e}^{-}\to K_S^0{K}_S^{0}J/\psi$ is $1.8\pm 0.6(\text{stat})\pm 0.3(\text{syst})\mathrm{pb}$ between 4.4 and 5.2 GeV. All of them are consistent with previously published results with improved precision. A search for resonant structures and associated intermediate states in the cross section of the process $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$ is performed.

Figure 1

Invariant mass distributions of (a) $e^{+}{e}^{-}$ and (b) ${\mu }^{+}{\mu }^{-}$ for selected $K^{+}{K}^{-}{\ell }^{+}{\ell }^{-}$ candidates. The curves show the best fits to the mass spectra, and the arrows show the required $J/\psi$ signal regions defined in the text.

Figure 2

The invariant mass distributions of the $K^{+}{K}^{-}J/\psi$ (a) and $K_S^0{K}_S^{0}J/\psi$ (b) candidates. The open histograms are from the $J/\psi$ signal region, while the shaded ones are from the $J/\psi$ mass sideband regions after a proper normalization.

Figure 3

(a) The distribution of the squared mass recoiling against the $K^{+}{K}^{-}J/\psi$ system distribution and (b) the polar angle distribution of the $K^{+}{K}^{-}J/\psi$ system in the $e^{+}{e}^{-}$ CM frame for the selected $K^{+}{K}^{-}J/\psi$ events with invariant masses between 4.0 and $6.0\mathrm{GeV}/c^2$. The points with error bars are data with the normalized $J/\psi$ mass sidebands subtracted; the solid histograms are MC simulated events.

Figure 4

The measured $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$ cross sections for CM energies up to 6.0 GeV (points with error bars). The errors are statistical and are determined by the numbers of signal and background events; a 7.8% systematic error that is common for all data points is not included.

Figure 5

Fits to the $K^{+}{K}^{-}J/\psi$ invariant mass distribution. The open histograms are the selected data in the $J/\psi$ signal region while the shaded histograms show the normalized $J/\psi$ sideband events. The solid curves show the best fit to the data and sideband background with one BW function (a) and the coherent sum of a BW function and the $\psi (4415)$ component (b).

Figure 6

Dalitz plots for the selected $K^{+}{K}^{-}J/\psi$ events for $4.4<M(K^{+}{K}^{-}J/\psi )<5.5\mathrm{GeV}/c^2$. The left panel is for events in the $J/\psi$ signal region while the right is from the $J/\psi$ mass sidebands (not normalized).

Figure 7

Invariant mass distributions of (a) $K^{+}{K}^{-}$, (b) $K^{+}J/\psi$, and (c) $K^{-}J/\psi$ for $K^{+}{K}^{-}J/\psi$ events with $4.4<M(K^{+}{K}^{-}J/\psi )<5.5\mathrm{GeV}/c^2$. Solid histograms are for events in the $J/\psi$ signal region, and the shaded histograms are normalized background from the $J/\psi$ mass sidebands.