Dalitz plot analysis of ${\eta }_c\to K^{+}{K}^{-}\eta$ and ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$ in two-photon interactions

We study the processes $\gamma \gamma \to K^{+}{K}^{-}\eta$ and $\gamma \gamma \to K^{+}{K}^{-}{\pi }^0$ using a data sample of $519{\mathrm{fb}}^{-1}$ recorded with the BABAR detector operating at the SLAC PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at center-of-mass energies at and near the $\mathit{\Upsilon }(nS)$ ($n=2,3,4$) resonances. We observe ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$ and ${\eta }_c\to K^{+}{K}^{-}\eta$ decays, measure their relative branching fraction, and perform a Dalitz plot analysis for each decay. We observe the $K_0^{*}(1430)\to K\eta$ decay and measure its branching fraction relative to the $K\pi$ decay mode to be $\mathcal{R}(K_0^{*}(1430))=\frac{\mathcal{B}(K_0^{*}(1430)\to K\eta )}{\mathcal{B}(K_0^{*}(1430)\to K\pi )}=0.092\pm 0.025_{-0.025}^{+0.010}$. The ${\eta }_c\to K^{+}{K}^{-}\eta$ and $K_0^{*}(1430)\to K\eta$ results correspond to the first observations of these channels. The data also show evidence for ${\eta }_c(2S)\to K^{+}{K}^{-}{\pi }^0$ and first evidence for ${\eta }_c(2S)\to K^{+}{K}^{-}\eta$.

Figure 1

Distributions of $p_T$ for (a) $\gamma \gamma \to K^{+}{K}^{-}\eta (\eta \to \gamma \gamma )$, (b) $\gamma \gamma \to K^{+}{K}^{-}\eta (\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)$, and (c) $\gamma \gamma \to K^{+}{K}^{-}{\pi }^0$. In each figure the data are shown as points with error bars, and the MC simulation is shown as a histogram; the vertical dashed line indicates the selection applied to isolate two-photon events.

Figure 2

Fitted detection efficiency in the $\cos \theta vs.m(K^{+}{K}^{-})$ plane for (a) ${\eta }_c\to K^{+}{K}^{-}\eta$ ($\eta \to \gamma \gamma$), (b) ${\eta }_c\to K^{+}{K}^{-}\eta$ ($\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ ), and (c) ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$. Each bin shows the average value of the fit in that region.

Figure 3

MC mass resolution for (a) ${\eta }_c\to K^{+}{K}^{-}\eta$ ($\eta \to \gamma \gamma$), (b) ${\eta }_c\to K^{+}{K}^{-}\eta$ ($\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ ), and (c) ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$. The curves represent the fits described in the text.

Figure 4

(a) The $K^{+}{K}^{-}\eta$ mass spectrum summed over the two $\eta$ decay modes. (b) The $K^{+}{K}^{-}{\pi }^0$ mass spectrum. In each figure, the solid curve shows the total fitted function and the dashed curve shows the fitted background contribution.

Figure 5

Dalitz plot for the ${\eta }_c\to K^{+}{K}^{-}\eta$ events in the signal region. The shaded area denotes the accessible kinematic region.

Figure 6

The ${\eta }_c\to K^{+}{K}^{-}\eta$ Dalitz plot projections. The superimposed curves result from the Dalitz plot analysis described in the text. The shaded regions show the background estimates obtained by interpolating the results of the Dalitz plot analyses of the sideband regions.

Figure 7

Legendre polynomial moments for ${\eta }_c\to K^{+}{K}^{-}\eta$ as a function of $K^{+}{K}^{-}$ mass. The superimposed curves result from the Dalitz plot analysis described in the text.

Figure 8

Legendre polynomial moments for ${\eta }_c\to K^{+}{K}^{-}\eta$ as a function of $K^{\pm }\eta$ mass. The superimposed curves result from the Dalitz plot analysis described in the text. The corresponding $K^{+}\eta$ and $K^{-}\eta$ distributions are combined.

Figure 9

Dalitz plot for the events in the ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$ signal region. The shaded area denotes the accessible kinematic region.

Figure 10

The ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$ Dalitz plot projections. The superimposed curves result from the Dalitz plot analysis described in the text. The shaded regions show the background estimates obtained by interpolating the results of the Dalitz plot analyses of the sideband regions.

Figure 11

Legendre polynomial moments for ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$ as a function of $K^{+}{K}^{-}$ mass. The superimposed curves result from the Dalitz plot analysis described in the text.

Figure 12

Legendre polynomial moments for ${\eta }_c\to K^{+}{K}^{-}{\pi }^0$ as a function of $K^{\pm }{\pi }^0$ mass. The superimposed curves result from the Dalitz plot analysis described in the text. The corresponding $K^{+}{\pi }^0$ and $K^{-}{\pi }^0$ distributions are combined.

Figure 13

Likelihood scans as functions of the $K_0^{*}(1430)$ (a) mass and (b) width. The horizontal (dotted) lines indicate the $\mathrm{\Delta }(-2\ln \mathcal{L})=1$ positions, the solid line the likelihood minimum, and the vertical (dashed) lines the uncertainty ranges.