Cross sections for the reactions $e^{+}{e}^{-}\to K_S^0{K}_L^0{\pi }^0$, $K_S^0{K}_L^0\eta$, and $K_S^0{K}_L^0{\pi }^0{\pi }^0$ from events with initial-state radiation

We study the processes $e^{+}{e}^{-}\to K_S^0{K}_L^0{\pi }^0\gamma$, $K_S^0{K}_L^0\eta \gamma$, and $K_S^0{K}_L^0{\pi }^0{\pi }^0\gamma$, where the photon is radiated from the initial state, providing cross section measurements for the hadronic final states over a continuum of center-of-mass energies. The results are based on $469{\mathrm{fb}}^{-1}$ of data collected at or near the $\mathrm{{\rm Y}}(4S)$ resonance with the BABAR detector at SLAC. We present the first measurements of the $e^{+}{e}^{-}\to K_S^0{K}_L^0{\pi }^0$, $K_S^0{K}_L^0\eta$, and $K_S^0{K}_L^0{\pi }^0{\pi }^0$ cross sections up to a center-of-mass energy of 4 GeV and study their intermediate resonance structures. We observe $J/\psi$ decays to all of these final states for the first time, present measurements of their $J/\psi$ branching fractions, and search for $\psi (2S)$ decays.

Figure 1

The ${\pi }^{+}{\pi }^{-}$ invariant mass distribution for the selected $K_S^0$ candidates in the data (points) and simulation (histogram). The vertical lines indicate the signal region.

Figure 2

Two-dimensional distribution of the higher cluster energy in a photon-candidate pair vs the corresponding diphoton mass $m_{\gamma \gamma }$ for all pairs of EMC clusters in $K_S^0{K}_L^0{\pi }^0\gamma$ events containing neither the ISR photon, the $K_L^0$ candidate, nor either photon in the ${\pi }^0$ candidate.

Figure 3

(a) The four-constraint ${\chi }^2$ distributions for data (points) and MC-simulated $K_S^0{K}_L^0{\pi }^0\gamma$ events (open histogram). The shaded, cross-hatched, and hatched areas represent the simulated backgrounds from non-ISR $q\overline{q}$, ISR $\varphi$, and ISR $\varphi \eta$ events, respectively. (b) The $K_S^0{K}_L^0{\pi }^0$ invariant mass distribution for data events in the signal region (points). The shaded, cross-hatched, and hatched areas represent the simulated contributions from non-ISR $q\overline{q}$, ISR $\varphi$, and ISR $\varphi \eta$ events, respectively, while the open histogram represents the total background estimated from the control region. (c) The $K_S^0{K}_L^0{\pi }^0$ invariant mass distribution after background subtraction (points). The open circles represent the contribution from the resonant process $e^{+}{e}^{-}\to K^{*}(892{)}^0{\overline{K}}^0+\mathrm{c}.\mathrm{c}.\to K_S^0{K}_L^0{\pi }^0$ (see text).

Figure 4

(a) The reconstructed $K_S^0{K}_L^0{\pi }^0$ invariant mass distribution for MC-simulated signal events in the signal (open histogram) and control (hatched) regions of Fig. 3. (b) The net reconstruction efficiency from the simulation.

Figure 5

The $e^{+}{e}^{-}\to K_S^0{K}_L^0{\pi }^0$ cross section. The error bars are statistical only.

Figure 6

The background-subtracted (a) $K_S^0{\pi }^0$ and (b) $K_L^0{\pi }^0$ invariant mass distributions in $e^{+}{e}^{-}\to K_S^0{K}_L^0{\pi }^0$ events. The curves represent the results of the fits described in the text, with the hatched areas representing the nonresonant components.

Figure 7

The $K_S^0{K}_L^0$ invariant mass distribution in selected $K_S^0{K}_L^0{\pi }^0$ events (dots) and the background estimated from the control region (hatched histogram) of Fig. 3. The solid line represents the result of the fit described in the text.

Figure 8

The $e^{+}{e}^{-}\to \varphi {\pi }^0$ cross section from this work (dots) compared with that obtained in the $K^{+}{K}^{-}{\pi }^0$ channel [15] (circles). The error bars are statistical only.

Figure 9

(a) The four-constraint ${\chi }^2$ distributions for data (points) and MC-simulated $K_S^0{K}_L^0\eta \gamma$ events (open histogram). The cross-hatched and hatched areas represent the simulated backgrounds from non-ISR $q\overline{q}$ events and the sum of ISR $K_S^0{K}_L^0{\pi }^0$, $K_S^0{K}_L^0$, and $K_S^0{K}_L^0{\pi }^0{\pi }^0$ events, respectively. (b) The $K_S^0{K}_L^0\eta$ invariant mass distribution for data events in the signal region (points). The cross-hatched and hatched areas represents simulated backgrounds from non-ISR $q\overline{q}$ and the sum of known ISR events, respectively, while the open histogram represents the total background, estimated from the control region. The curve shows the empirical fit used for background subtraction. (c) The $K_S^0{K}_L^0\eta$ invariant mass distribution after background subtraction (points). The open circles represent the contribution from the resonant process $e^{+}{e}^{-}\to \varphi \eta \to K_S^0{K}_L^0\eta$ (see text).

Figure 10

The $e^{+}{e}^{-}\to K_S^0{K}_L^0\eta$ cross section.

Figure 11

The background-subtracted $K_S^0{K}_L^0$ invariant mass distribution in $e^{+}{e}^{-}\to K_S^0{K}_L^0\eta$ events (points), compared with that of simulated $e^{+}{e}^{-}\to \varphi \eta$ events (histogram), normalized to number of experimental events.

Figure 12

The $e^{+}{e}^{-}\to \varphi (1020)\eta$ cross section obtained from this work (solid dots), compared with the previous BABAR measurement in the $K^{+}{K}^{-}\eta$ final state [15] (open circles). Only statistical errors are shown.

Figure 13

(a) The five-constraint ${\chi }^2$ distributions for data (points) and MC-simulated $K_S^0{K}_L^0{\pi }^0{\pi }^0\gamma$ events (open histogram). The cross-hatched and hatched areas represent the simulated backgrounds from non-ISR $q\overline{q}$ and the sum of ISR $K_S^0{K}_L^0$, $K_S^0{K}_L^0{\pi }^0$, and $K_S^0{K}_L^0\eta$ events, respectively. (b) The $K_S^0{K}_L^0{\pi }^0{\pi }^0$ invariant mass distribution for data events in the signal region of (a) (points). The cross-hatched and hatched areas represent the simulated contributions from non-ISR $q\overline{q}$ events and the sum of known ISR events, respectively, and the open squares represent the additional background estimated from the control region. The curves show the empirical fits used for background subtraction. (c) The $K_S^0{K}_L^0{\pi }^0{\pi }^0$ invariant mass distribution after subtraction of all backgrounds.

Figure 14

The $e^{+}{e}^{-}\to K_S^0{K}_L^0{\pi }^0{\pi }^0$ cross section.

Figure 15

The (a) $K_S^0{\pi }^0$ and (b) $K_L^0{\pi }^0$ invariant mass distributions for selected $K_S^0{K}_L^0{\pi }^0{\pi }^0$ events in the data (points). The curves represent the results of the fits described in the text, with the hatched areas representing the nonresonant components.

Figure 16

Expanded views of the invariant mass distributions in the charmonium mass region for the (a) $K_S^0{K}_L^0{\pi }^0$, (b) $K_S^0{K}_L^0\eta$, and (c) $K_S^0{K}_L^0{\pi }^0{\pi }^0$ final states. The lines represent the results of the fits described in the text.

Figure 17

The $K_S^0{K}_L^0{\pi }^0$ invariant mass distributions for events in which the $K_S^0{\pi }^0$ or $K_L^0{\pi }^0$ mass is within $0.15\mathrm{GeV}/c^2$ of (a) the nominal $K^{*}(892{)}^0$ mass or (b) the nominal $K_2^{*}(1430{)}^0$ mass. The lines represent the results of the fits described in the text.