Measurement of the $e^{+}{e}^{-}\to K_s^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ and $K_s^0{K}^{\pm }{\pi }^{\mp }\eta$ cross sections using initial-state radiation

The processes $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ and $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }\eta$ are studied over a continuum of energies from threshold to 4 GeV with the initial-state photon radiation method. Using $454{\text{fb}}^{-1}$ of data collected with the BABAR detector at the SLAC PEP-II storage ring, the first measurements of the cross sections for these processes are obtained. The intermediate resonance structures from $K^{*0}(K\pi {)}^0$, $K^{*}(892{)}^{\pm }(K\pi {)}^{\mp }$, and $K_S^0{K}^{\pm }{\rho }^{\mp }$ are studied. The $J/\psi$ is observed in all of these channels, and corresponding branching fractions are measured.

Figure 1

Distribution of ${\chi }^2$ from the five-constraint fit for $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0\gamma$ candidates in the data (points). The open and cross-hatched histograms are the distributions for simulated signal and $q\overline{q}$ background events, respectively, normalized as described in the text. The signal and control regions are indicated.

Figure 2

The (a) $\gamma \gamma$ and (b) ${\pi }^{+}{\pi }^{-}$ invariant-mass distributions of the ${\pi }^0$ and $K_S^0$ candidates, respectively, in $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ events in the ${\chi }_{K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0}^2$ signal region, for the selected data (points) and the signal simulation (histograms).

Figure 3

Distribution of the fitted $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ invariant mass for data events in the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ signal region. The hatched and cross-hatched distributions show the estimated backgrounds evaluated from ISR and $q\overline{q}$ events, respectively.

Figure 4

The ${\chi }_{K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0}^2$ distributions of the ISR background determined from the data (points with errors) and the sum of MC simulations for the processes $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }\gamma$ and $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0{\pi }^0\gamma$ (open histogram) described in the text.

Figure 5

Detection efficiency for $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ events as a function of the hadronic invariant mass $E_{\mathrm{c}.\mathrm{m}.}=m(K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0)$. The solid curve shows a fitted parametrization.

Figure 6

Cross section for the process $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$. The uncertainties are statistical.

Figure 7

Scatter plots of (a) the $K_S^0{\pi }^0$ vs $K^{\pm }{\pi }^{\mp }$ and (b) $K^{\pm }{\pi }^0$ vs $K_S^0{\pi }^{\mp }$ invariant masses in $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ events.

Figure 8

The (a) $K_S^0{\pi }^0$ and (b) $K^{\pm }{\pi }^{\mp }$ invariant-mass projections of Fig. 7 and the (c) $K_S^0{\pi }^{\pm }$ and (d) $K^{\pm }{\pi }^0$ invariant-mass projections of Fig. 7. The lines represent the results of the fits described in the text, with the hatched areas denoting their nonresonant components.

Figure 9

Cross sections for (a) the processes $e^{+}{e}^{-}\to K^{*0}{K}^{\pm }{\pi }^{\mp }$ (squares), $e^{+}{e}^{-}\to K^{*0}{K}_S^0{\pi }^0$ (triangles), and $e^{+}{e}^{-}\to K^{*0}\overline{K}{}^{*0}$ (circles) and (b) the processes $e^{+}{e}^{-}\to K^{*}(892{)}^{\pm }{K}_S^0{\pi }^{\mp }$ (squares), $e^{+}{e}^{-}\to K^{*}(892{)}^{\pm }{K}^{\mp }{\pi }^0$ (triangles), and $e^{+}{e}^{-}\to K^{*}(892{)}^{+}{K}^{*}(892{)}^{-}$ (circles). The uncertainties are statistical only, and in each case, the $K^{*}\overline{K}{}^{*}$ cross section is included in both of the others.

Figure 10

The number of events in the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ sample containing (a) a $K^{*0}\to K^{\pm }{\pi }^{\mp }$ decay as a function of the $K_S^0{\pi }^0$ invariant mass and (b) a $K^{*}(892{)}^{\pm }\to K_S^0{\pi }^{\pm }$ decay as a function of the $K^{\pm }{\pi }^0$ invariant mass. The lines represent the result of the fits described in the text, with the hatched areas denoting their nonresonant components.

Figure 11

(a) The ${\pi }^{\pm }{\pi }^0$ invariant-mass distribution in $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ events. The line represents the result of the fit described in the text, with the hatched area denoting its nonresonant component. (b) Cross section for the process $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\rho }^{\mp }$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$. The uncertainties are statistical only.

Figure 12

The (a) $K^{\pm }{\pi }^{\mp }{\pi }^0$ and (b) $K_S^0{\pi }^{\pm }{\pi }^0$ invariant-mass distributions in $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ events. The solid lines represent the results of the fits described in the text; the hatched areas denote their nonresonant components, while the dashed, dotted, and dash-dotted lines indicate the contributions from $K{K}_1(1270)$, $K{K}_1(1400)$, and $K{K}_1(1650)$ events, respectively.

Figure 13

Distribution of ${\chi }^2$ from the five-constraint fit of the $K_S^0{K}^{\pm }{\pi }^{\mp }\eta \gamma$ candidates in the data (points). The open and cross-hatched histograms are the distributions for simulated signal and $q\overline{q}$ background events, respectively, normalized as described in the text. The signal and control regions are indicated.

Figure 14

The (a) $\gamma \gamma$ and (b) ${\pi }^{+}{\pi }^{-}$ invariant-mass distributions of the $\eta$ and $K_S^0$ candidates, respectively, in $K_S^0{K}^{\pm }{\pi }^{\mp }\eta$ events in the ${\chi }_{K_S^0{K}^{\pm }{\pi }^{\mp }\eta }^2$ signal region, for the selected data (points) and the signal simulation (histograms).

Figure 15

Distribution of the fitted $K_S^0{K}^{\pm }{\pi }^{\mp }\eta$ invariant mass for data events in the signal region (open histogram). The hatched and cross-hatched distributions show the estimated backgrounds evaluated from the control region and from $q\overline{q}$ events, respectively.

Figure 16

Detection efficiency for $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }\eta$ events as a function of the hadronic invariant mass $E_{\mathrm{c}.\mathrm{m}.}=m(K_S^0{K}^{\pm }{\pi }^{\mp }\eta )$. The solid curve shows the fitted parametrization.

Figure 17

Cross section for the process $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }\eta$. Uncertainties are statistical.

Figure 18

The (a) $K_S^0{\pi }^{\pm }$ and (b) $K^{\pm }{\pi }^{\mp }$ invariant-mass distributions in $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }\eta$ events. The lines represent the results of the fits described in the text.

Figure 19

Cross sections for the processes (a) $e^{+}{e}^{-}\to K^{*}(892{)}^{\pm }{K}^{\mp }\eta$ and (b) $e^{+}{e}^{-}\to K^{*}(892{)}^0{K}_S^0\eta$. The uncertainties are statistical only.

Figure 20

The $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ invariant-mass distribution in the $J/\psi$ mass region. The line represents the result of the fit described in the text, with the open (hatched) area indicating the (non)resonant component.

Figure 21

The $K_S^0{K}^{\pm }{\pi }^{\mp }\eta$ invariant-mass distribution in the $J/\psi$ mass region. The line represents the result of the fit described in the text, with the open (hatched) area indicating the (non)resonant component.

Figure 22

The number of $K_S^0{K}^{\pm }{\rho }^{\mp }$ events as a function of the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ invariant mass in the $J/\psi$ region. The line represents the result of the fit described in the text, with the open (hatched) area indicating the resonant (nonresonant) component.

Figure 23

Event yields of (a) $K^{*0}{K}_S^0{\pi }^0$, (b) $K^{*0}{K}^{\pm }{\pi }^{\mp }$, (c) $K^{*\pm }{K}^{\mp }{\pi }^0$, and (d) $K^{*\pm }{K}_S^0{\pi }^{\mp }$ final states as functions of the $K_S^0{K}^{\pm }{\pi }^{\mp }{\pi }^0$ invariant mass in the $J/\psi$ region. The lines represent the results of the fits described in the text, with the open (hatched) areas indicating the resonant (nonresonant) components.