Dalitz plot analyses of $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$, $J/\psi \to K^{+}{K}^{-}{\pi }^0$, and $J/\psi \to K_s^0{K}^{\pm }{\pi }^{\mp }$ produced via $e^{+}{e}^{-}$ annihilation with initial-state radiation

We study the processes $e^{+}{e}^{-}\to {\gamma }_{\mathrm{ISR}}J/\psi$, where $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$, $J/\psi \to K^{+}{K}^{-}{\pi }^0$, and $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$ 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 $\mathrm{{\rm Y}}(nS)$ ($n=2,3,4$) resonances. We measure the ratio of branching fractions ${\mathcal{R}}_1=\frac{\mathcal{B}(J/\psi \to K^{+}{K}^{-}{\pi }^0)}{\mathcal{B}(J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0)}$ and ${\mathcal{R}}_2=\frac{\mathcal{B}(J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp })}{\mathcal{B}(J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0)}$. We perform Dalitz plot analyses of the three $J/\psi$ decay modes and measure fractions for resonances contributing to the decays. We also analyze the $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay using the Veneziano model. We observe structures compatible with the presence of $\rho (1450)$ in all three $J/\psi$ decay modes and measure the relative branching fraction: $\mathcal{R}(\rho (1450))=\frac{\mathcal{B}(\rho (1450)\to K^{+}{K}^{-})}{\mathcal{B}(\rho (1450)\to {\pi }^{+}{\pi }^{-})}=0.307\pm 0.084(\text{stat})\pm 0.082(\text{sys})$.

Figure 1

(a) Distribution of ${\theta }_{\mathrm{ISR}}$ for events in the $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ ISR signal region. The dashed line indicates the ${\theta }_{\mathrm{ISR}}=23^0$ angle.

Figure 2

Distributions of $M_{\mathrm{rec}}^2$ for $e^{+}{e}^{-}\to {\gamma }_{\mathrm{ISR}}J/\psi$, where (a) $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$, (b) $J/\psi \to K^{+}{K}^{-}{\pi }^0$, and (c) $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$. In each figure the data are shown as points with error bars, and the MC simulation is shown as a histogram.

Figure 3

(a) The ${\pi }^{+}{\pi }^{-}{\pi }^0$, (b) $K^{+}{K}^{-}{K}^0$, and $K_S^0{K}^{\pm }{\pi }^{\mp }$ mass spectra in the ISR region. In each figure, the solid curve shows the total fit function and the dashed curve shows the fitted background contribution.

Figure 4

Fitted detection efficiency in the $\cos {\theta }_h$ vs $m_{12}$ plane for (a) $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$, (b) $J/\psi \to K^{+}{K}^{-}{\pi }^0$, and (c) $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$. Each bin shows the average value of the fit in that region.

Figure 5

Dalitz plot for the $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ events in the signal region.

Figure 6

The $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ 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 7

(a) Binned scatter diagram of $\cos {\theta }_{{\pi }_3}$ vs $m({\pi }_1{\pi }_2)$. (b) and (c) $\pi \pi$ mass projection in the $|\cos {\theta }_{\pi }|<0.2$ region for all the three $\pi \pi$ charge combinations. The horizontal lines in (a) indicate the $\cos {\theta }_{\pi }$ selection. The dashed line in (b) is the result from the fit with only the $\rho (770)\pi$ amplitude. The fit in (b) uses the isobar model and the shaded histogram shows the background distribution estimated from the $J/\psi$ sidebands. The fit in (c) uses the Veneziano model.

Figure 8

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

Figure 9

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

Figure 10

Dalitz plot for the $J/\psi \to K^{+}{K}^{-}{\pi }^0$ events in the signal region.

Figure 11

The $J/\psi \to K^{+}{K}^{-}{\pi }^0$ 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 12

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

Figure 13

Legendre polynomial moments for $J/\psi \to K^{+}{K}^{-}{\pi }^0$ 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 14

Dalitz plot for the $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$ events in the signal region.

Figure 15

The $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$ 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 16

Legendre polynomial moments for $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$ as a function of $K_S^0{K}^{\pm }$ mass. The superimposed curves result from the Dalitz plot analysis described in the text.

Figure 17

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