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

This paper reports measurements of processes: $e^{+}{e}^{-}\to \gamma K_S^0{K}^{\pm }{\pi }^{\mp }$, $e^{+}{e}^{-}\to \gamma K^{+}{K}^{-}{\pi }^0$, $e^{+}{e}^{-}\to \gamma \varphi \eta$, and $e^{+}{e}^{-}\to \gamma \varphi {\pi }^0$. The initial-state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to $\approx 4.6\mathrm{GeV}$. The overall size of the data sample analyzed is $232{\mathrm{fb}}^{-1}$, collected by the BABAR detector running at the PEP-II $e^{+}{e}^{-}$ storage ring. From the Dalitz plot analysis of the $K_S^0{K}^{\pm }{\pi }^{\mp }$ final state, moduli, and relative phase of the isoscalar and the isovector components of the $e^{+}{e}^{-}\to K{K}^{*}(892)$ cross section are determined. Parameters of $\varphi$ and $\rho$ recurrences are also measured, using a global fitting procedure which exploits the interconnection among amplitudes, moduli, and phases of the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }$, $K^{+}{K}^{-}{\pi }^0$, $\varphi \eta$ final states. The cross section for the OZI-forbidden process $e^{+}{e}^{-}\to \varphi {\pi }^0$, and the $J/\psi$ branching fractions to $K{K}^{*}(892)$ and $K^{+}{K}^{-}\eta$ are also measured.

Figure 1

The ${\chi }^2$ distributions for data (points), signal MC (open histogram) normalized to the first bin of the data, background contribution due to $q\overline{q}$ (hatched histogram), and different ISR-produced final states (gray histogram).

Figure 2

Reconstructed $K_S^0$ mass for data (points) and signal MC simulation (histogram).

Figure 3

(a) Invariant mass of the ISR photon and any other photon in the event. Distributions for data (points with error bars), signal MC (open histogram), and $q\overline{q}$ MC (hatched histogram) samples are shown. (b) $\gamma \gamma$ mass distribution for additional photons in data (points) compared with signal MC simulation.

Figure 4

The invariant mass distribution of the $K_S^0{K}^{\pm }{\pi }^{\mp }$ system (open histogram). The hatched and gray histograms show the $q\overline{q}$ and ISR backgrounds, respectively.

Figure 5

Detection and reconstruction efficiency as a function of the c.m. energy for the $K_S^0{K}^{\pm }{\pi }^{\mp }$ final state. The solid line is the result of a linear fit to the data.

Figure 6

The $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }$ cross section. Inset: expanded view in the mass range $3.2<E_{\mathrm{c}.\mathrm{m}.}<4.6\mathrm{GeV}$.

Figure 7

Comparison of the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }$ cross section measured in BABAR with previous experiments, in the mass range $1.3<E_{\mathrm{c}.\mathrm{m}.}<2.4\mathrm{GeV}$.

Figure 8

The ${\chi }^2$ distributions for data (points), signal MC simulation (open histogram) normalized to the first bin of the data, background contributions due to $q\overline{q}$ (hatched histogram), and to $e^{+}{e}^{-}\to \omega \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ MC simulation (gray histogram).

Figure 9

The invariant mass distribution of the $K^{+}{K}^{-}{\pi }^0$ system (open histogram). The hatched and gray histograms show the $q\overline{q}$ and ISR backgrounds, respectively.

Figure 10

Detection and reconstruction efficiency as a function of the c.m. energy for $K^{+}{K}^{-}{\pi }^0$ final state. The solid line is the result of a fit to the data with the function $a(1-(x/b{)}^p·e^{\xi (b-x)})$, where $x=E_{\mathrm{c}.\mathrm{m}.}$.

Figure 11

The $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0$ cross section. Inset: expanded view in the $3.2<E_{\mathrm{c}.\mathrm{m}.}<4.6\mathrm{GeV}$ mass range.

Figure 12

Comparison of the $e^{+}{e}^{-}\to K^{+}{K}^{-}{\pi }^0$ cross section measured in BABAR with previous experiments.

Figure 13

The Dalitz plot distribution for the $K^{+}{K}^{-}{\pi }^0$ final state.

Figure 14

The Dalitz plot distribution for the $K_S^0{K}^{\pm }{\pi }^{\mp }$ final state.

Figure 15

(a) Dalitz plot distributions for $K_S^0{K}^{\pm }{\pi }^{\mp }$ events with an invariant mass $M_{K_S^{0}K\pi }<2.0\mathrm{GeV}/c^2$. (b) $K_S^0{\pi }^{\pm }$ projection, with the broad charged $K^{*}(892)$ peak, (c) $K^{\pm }{\pi }^{\mp }$ projection, with the narrow neutral $K^{*}(892)$ peak. (d) $K_S^0{K}^{\pm }$ projection.

Figure 16

Isoscalar component of the cross section for the process $e^{+}{e}^{-}\to K^{*}(892)K$. The vertical line indicates the separation between the two regions used in the analysis.

Figure 17

Isovector component of the cross section for the process $e^{+}{e}^{-}\to K^{*}(892)K$. The vertical line indicates the separation between the two regions used in the analysis.

Figure 18

Relative phase between the isoscalar and isovector component of the $e^{+}{e}^{-}\to K^{*}(892)K$ cross section.

Figure 19

(a) Dalitz plot distributions for $K_S^0{K}^{\pm }{\pi }^{\mp }$ events with an invariant mass $M_{K_S^{0}K\pi }>2.0\mathrm{GeV}/c^2$. (b) $K_S^0{\pi }^{\pm }$ projection, with the broad charged $K_2^{*}(1430)$ peak. (c) $K^{\pm }{\pi }^{\mp }$ projection, with the narrow neutral $K^{*}(892)$ peak. (d) $K_S^0{K}^{\pm }$ projection.

Figure 20

Isoscalar (a) and isovector (b) components of the cross section for the process $e^{+}{e}^{-}\to K_2^{*}(1430)K$.

Figure 21

The isospin amplitudes (defined as the square root of the isospin components divided by the phase space) for the $K_S^0{K}^{\pm }{\pi }^{\mp }$ channel, obtained by fitting the Dalitz plot in the region $E_{\mathrm{c}.\mathrm{m}.}>2.0\mathrm{GeV}$, in the case of $K_2^{*}(1430)K$ intermediate state.

Figure 22

(a) $K_S^0{K}^{\pm }{\pi }^{\mp }$ mass distribution in the $J/\psi$ mass region. (b–d) Mass distributions of selected events for: (b) $K^{*0}(892)K_S^0(K^{*0}(892)\to K^{\pm }{\pi }^{\mp })$; (c) $K^{*\pm }(892)K^{\mp }(K^{*\pm }(892)\to K_S^0{\pi }^{\pm })$; and (d) $K^{*\pm }(892)K^{\mp }(K^{*\pm }(892)\to K^{\pm }{\pi }^0)$. The curves represent the fits obtained using a sum of two Gaussians and a linear function.

Figure 23

The 2-dimensional $K^{+}{K}^{-}$, $\gamma \gamma$ invariant mass distribution around the $\varphi$ and ${\pi }^0$ masses. The central cell identifies the signal region.

Figure 24

The $K^{+}{K}^{-}$ (a) and $\gamma \gamma$ (b) invariant mass distributions. Signal and sideband regions are set by vertical lines in the plots.

Figure 25

The invariant mass distribution of the $\varphi {\pi }^0$ system (open histogram). The hatched and gray histograms show the background from non-$\varphi$ $K^{+}{K}^{-}{\pi }^0$ and from $\gamma \gamma$ combinatorial.

Figure 26

Detection and reconstruction efficiency as a function of the c.m. energy for the $\varphi {\pi }^0$ final state. The solid line is the result of a fit to the data with the function $a(1-(x/b{)}^p·e^{\xi (b-x)})$, where $x=E_{\mathrm{c}.\mathrm{m}.}$.

Figure 27

The $e^{+}{e}^{-}\to \varphi {\pi }^0$ cross section.

Figure 28

The $K^{+}{K}^{-}$ (a) and $\gamma \gamma$ (b) invariant mass distributions for selected events.

Figure 29

The invariant mass distribution of the $K^{+}{K}^{-}\eta$ system (open histogram). The hatched and the gray histograms show the $q\overline{q}$ and ISR backgrounds, respectively.

Figure 30

The $e^{+}{e}^{-}\to K^{+}{K}^{-}\eta$ cross section as a function of c.m. energy.

Figure 31

(a) The $\gamma \gamma$ invariant mass distribution in the $\eta$ region, when a $J/\psi \to K^{+}{K}^{-}\eta$ decay is selected. (b) The final $J/\psi$ signal ($0.513<M_{\gamma \gamma }<0.583\mathrm{GeV}/c^2$ required).

Figure 32

The $K^{+}{K}^{-}$ (a) and $\gamma \gamma$ (b) invariant mass distributions. Signal and sideband regions are set by vertical lines in the plots.

Figure 33

The invariant mass distribution of the $\varphi \eta$ system. The shaded histogram refers to the small subtracted background component.

Figure 34

Detection and reconstruction efficiency as a function of the c.m. energy for the $\varphi \eta$ final state. The solid line is the result of a fit to the data with the function $a(1-(x/b{)}^p·e^{\xi (b-x)})$, where $x=E_{\mathrm{c}.\mathrm{m}.}$.

Figure 35

The $e^{+}{e}^{-}\to \varphi \eta$ cross section distribution as a function of c.m. energy.

Figure 36

Phase difference between isovector and isoscalar $K{K}^{*}(892)$ amplitudes: data and fits superimposed (dark-gray and hatched bands). In particular the dark-gray band is obtained by using only our $\varphi \eta$ cross section, while the hatched band includes also the data from Ref. 25. The light-gray band represents the relative phase expected in case of nonresonant isovector component.

Figure 37

Isoscalar (a) and isovector (b) components of the $K_S^0{K}^{\pm }{\pi }^{\mp }$ cross section. The solid points are the data and the bands represent the fits. The hatched band is obtained including the $\varphi \eta$ cross section from Ref. 25.

Figure 38

Data on the annihilation cross section ${\sigma }_{K^{\pm }{K}^{*\mp }(892)}$, see Eq. (13), and descriptions (solid and hatched bands) in terms of the parametrization of Eq. (11), with parameters reported in Table . The hatched band is obtained including the $\varphi \eta$ cross section from Ref. 25.

Figure 39

Data on the annihilation cross section ${\sigma }_{\varphi \eta }$ (the solid circles are from this analysis, while the empty squares are from Ref. 25) and descriptions (solid and hatched bands) in terms of the parametrization of Eq. (11), with parameters reported in Table . The hatched band is obtained including the $\varphi \eta$ cross section from Ref. 25.

Figure 40

Data on the annihilation cross section ${\sigma }_{\varphi {\pi }^0}$ and descriptions in terms of the parametrization of Eq. (11) with the only ${\rho }^{\prime \prime }$, hatched band, and including also the $\rho (1900)$, gray band.