Study of the reactions $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0$, $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0$, and $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$ at center-of-mass energies from threshold to 4.5 GeV using initial-state radiation

We study the processes $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0\gamma$, $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0\gamma$, and $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}\gamma$ in which an energetic photon is radiated from the initial state. The data were collected with the BABAR detector at the SLAC National Accelerator Laboratory. About 1200, 2600, and 6000 events, respectively, are selected from a data sample corresponding to an integrated luminosity of $469{\mathrm{fb}}^{-1}$. The invariant mass of the hadronic final state defines the effective $e^{+}{e}^{-}$ center-of-mass energy. The center-of-mass energies range from threshold to 4.5 GeV. From the mass spectra, the first ever measurements of the $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0$, $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0$, and $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$ cross sections are performed. The contributions from the intermediate states that include $\eta$, $\varphi$, $\rho$, $K^{*}(892)$, and other resonances are presented. We observe the $J/\psi$ and $\psi (2S)$ in most of these final states and measure the corresponding branching fractions, many of them for the first time.

Figure 1

The $m(\gamma \gamma )$ invariant mass for the third photon pair (a) in the $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0\gamma \gamma {\gamma }_{\mathrm{ISR}}$ hypothesis and (b) in the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0\gamma \gamma {\gamma }_{\mathrm{ISR}}$ hypothesis for the ${\chi }^2$ signal regions. The dashed histograms are for events from the ${\chi }^2$ control regions. The dotted histograms are for the remaining $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\gamma }_{\mathrm{ISR}}$ or $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\gamma }_{\mathrm{ISR}}$ backgrounds from simulation. (c) The ${\chi }_{K_S^{0}K3\pi }^2$ distribution in the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}{\gamma }_{\mathrm{ISR}}$ hypothesis for data (solid histogram) and for the MC simulation (dashed). The shaded histogram is for the $uds$ backgrounds, and single bins are for the remaining contribution from the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\gamma }_{\mathrm{ISR}}$ process.

Figure 2

(a) Third photon pair $m(\gamma \gamma )$ invariant mass for the MC simulated $\varphi \eta$ events after applied selections and background subtraction (solid histogram). The dashed histogram shows the contribution of the subtracted events from the ${\chi }^2$ control region. The curve is for the three-Gaussian fit to the ${\pi }^0$ signal. (b) Background-subtracted ${\pi }^0{\pi }^0{\pi }^0$ invariant mass distribution (solid histogram) for the MC simulated $\varphi \eta$ final state, and the events from the ${\chi }^2$ control region (dashed histogram). The solid curve is fit to the $\eta$ signal. (c) Background-subtracted second photon pair invariant mass (solid histogram) for the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0$ final state with the three-Gaussian fit function. The dashed histogram shows the contribution from the ${\chi }^2$ control region.

Figure 3

Hadronic invariant-mass-dependent reconstruction efficiency for (a) the $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0{\gamma }_{\mathrm{ISR}}$ events, (b) the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0{\gamma }_{\mathrm{ISR}}$ events, and (c) the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}{\gamma }_{\mathrm{ISR}}$ events. The curves show the fit results, which are used in the cross section calculation.

Figure 4

Number of events determined from the ${\pi }^0$ fit vs the hadronic invariant mass for the (a) $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0$ and (b) $e^{+}{e}^{-}\to K_S^{0}K\pi {\pi }^0{\pi }^0$ reactions. The contributions from $uds$ events are shown by (red) squares. (c) Number of $e^{+}{e}^{-}\to K_S^{0}K\pi {\pi }^{+}{\pi }^{-}$ events in the ${\chi }^2$ signal (solid histogram) and control (dashed) regions. The shaded histogram shows the contribution from the $uds$ events.

Figure 5

Measured (a) $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0$, (b) $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0$, and (c) $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$ cross sections. The uncertainties are statistical only.

Figure 6

For the $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0$ reaction: (a) $m(3{\pi }^0)$ invariant mass distribution for the ${\chi }^2$ signal (dots) and control (histogram) regions. The curve shows a fit to the $\eta \to {\pi }^0{\pi }^0{\pi }^0$ signal. The dashed line shows the combinatorial background. (b) The $m(K^{+}{K}^{-})$ invariant mass distribution for events with $m(3{\pi }^0)<0.7$ from (a). (c) The $m(K^{\pm }{\pi }^0)$ invariant mass distribution (six entries/event). The curve shows a fit to the $K^{*}(892)$ signal.

Figure 7

Measured (a) $e^{+}{e}^{-}\to K^{+}{K}^{-}\eta$, (b) $e^{+}{e}^{-}\to \varphi \eta$, and (c) $e^{+}{e}^{-}\to K^{*+}{K}^{*-}{\pi }^0$ cross sections. The uncertainties are statistical only.

Figure 8

(a) $m(K^{\pm }{\pi }^{\mp })$, (b) $m(K_S^0{\pi }^{\pm })$, and (c) $m({\pi }^{\pm }{\pi }^0)$ invariant mass distributions for the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0$ events. The curves show the fit to the $K^{*}(892)$ and $\rho (770)$ signals with the combinatoric background contribution shown by the dashed curves.

Figure 9

Measured (a) $e^{+}{e}^{-}\to K_S^0{K}^{*0}{\pi }^0{\pi }^0$, (b) $e^{+}{e}^{-}\to K^{*\pm }{K}^{\mp }{\pi }^0{\pi }^0$, and (c) $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\rho }^{\mp }{\pi }^0$ cross sections. The uncertainties are statistical only.

Figure 10

(a) $m(K^{\pm }{\pi }^{\mp })$, (b) $m(K_S^0{\pi }^{\pm })$, and (c) $m({\pi }^{\pm }{\pi }^0)$ invariant mass distributions for the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$ events. The curves show fits to (a, b) the $K^{*}(892)$ signal and to (c) the $\rho (770)$ signal. The dashed curves indicate the combinatoric background.

Figure 11

Observed mass dependence for the (a) $e^{+}{e}^{-}\to K_S^0{K}^{*0}{\pi }^{+}{\pi }^{-}$, (b) $e^{+}{e}^{-}\to K^{*\pm }{K}^{\mp }{\pi }^{+}{\pi }^{-}$, and (c) $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\rho }^0{\pi }^{\mp }$ reactions. The contribution from the $uds$ reaction is shown by squares.

Figure 12

(a) $m(K_S^0{K}^{\pm }{\pi }^{\mp })$ invariant mass distribution. The solid curve is the fit to the $f_1(1285)$ signal with the combinatorial background, shown by the dashed curve. (b) Scatter plot for the $m({\pi }^{+}{\pi }^{-})$ vs $m(K_S^0{K}^{\pm }{\pi }^{\mp })$ invariant mass.

Figure 13

Measured $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ cross section from the present analysis (dots) in comparison with previous measurements (squares) [12]. The solid curve is the fit explained in the text.

Figure 14

(a) $m(K_S^{0}K3\pi )$ invariant mass distribution. The solid curve shows the fit to the $X(2400)$ signal with a combinatorial background, shown by the dashed curve. (b) Sum of events from the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$, $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{\pi }^0$, and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0{\pi }^0$ reactions. The fit is the same as for (a).

Figure 15

(a) $m(K_S^{0}K3\pi )$ invariant mass distribution around $2.17\mathrm{GeV}/c^2$. The curves are fits to the $\varphi (2170)$ signal with a combinatorial background. (b) Same as (a) with the additional requirement $m({\pi }^{+}{\pi }^{-})<0.7\mathrm{GeV}/c^2$. The solid curve is a fit to the $\varphi (2170)$ signal, with the combinatorial background shown by the dashed curve.

Figure 16

The $J/\psi$ invariant mass region for the (a) $K^{+}{K}^{-}{\pi }^0{\pi }^0{\pi }^0$, (b) $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0$, and (c) $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$ events. The curves show the fit functions described in the text.

Figure 17

(a) $m(K_S^{0}K\pi )$ invariant mass vs $m(K_S^{0}K3\pi )$ invariant mass for the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^{+}{\pi }^{-}$ events around the $\psi (2S)$ signal. (b) $m(K_S^{0}K3\pi )$ invariant mass distribution with the $J/\psi$ selection in the $K_S^0{K}^{\pm }{\pi }^{\mp }$ invariant mass. The solid curve shows the fit to the $\psi (2S)$ signal, with a linear background shown by the dashed line.