Search for resonances decaying to ${\eta }_c{\pi }^{+}{\pi }^{-}$ in two-photon interactions

We report a study of the process $\gamma \gamma \to X\to {\eta }_c{\pi }^{+}{\pi }^{-}$, where $X$ stands for one of the resonances ${\chi }_{c2}(1P)$, ${\eta }_c(2S)$, $X(3872)$, $X(3915)$, or ${\chi }_{c2}(2P)$. The analysis is performed with a data sample of $473.9{\mathrm{fb}}^{-1}$ collected with the BABAR detector at the PEP-II asymmetric-energy electron-positron collider. We do not observe a significant signal for any channel, and calculate 90% confidence-level upper limits on the products of branching fractions and two-photon widths ${\Gamma }_{X\to \gamma \gamma }\mathcal{B}(X\to {\eta }_c{\pi }^{+}{\pi }^{-})$: 15.7 eV for ${\chi }_{c2}(1P)$, 133 eV for ${\eta }_c(2S)$, 11.1 eV for $X(3872)$ (assuming it to be a spin-2 state), 16 eV for $X(3915)$ (assuming it to be a spin-2 state), and 18 eV for ${\chi }_{c2}(2P)$. We also report upper limits on the ratios of branching fractions $\mathcal{B}({\eta }_c(2S)\to {\eta }_c{\pi }^{+}{\pi }^{-})/\mathcal{B}({\eta }_c(2S)\to K_S^0{K}^{+}{\pi }^{-})<10.0$ and $\mathcal{B}({\chi }_{c2}(1P)\to {\eta }_c{\pi }^{+}{\pi }^{-})/\mathcal{B}({\chi }_{c2}(1P)\to K_S^0{K}^{+}{\pi }^{-})<32.9$ at the 90% confidence level.

Figure 1

(a) The $m(K_S^0{K}^{+}{\pi }^{-})$ distribution for the control sample. The vertical lines indicate the ${\eta }_c$ peak mass region. Also shown are the $K_S^0{K}^{+}{\pi }^{-}$ Dalitz plots for (b) control-sample events in the ${\eta }_c$ peak mass region and for main-sample events in the (c) lower and (d) upper ${\eta }_c$ mass sidebands. Solid black lines indicate the regions defined by the Dalitz-plot selection criteria. The dotted blue box in the upper left corner of (c) and (d) indicates the Dalitz-plot-sideband background region used for the neural-network training.

Figure 2

Signal (unhatched) and background (hatched) distributions of the neural-network input variables (a) $E_{\mathrm{ex}}$, (b) $p_X^T$, and the (c) kaon and (d) pion identification variables. (e) The distributions of the neural-network output variable $V_{\mathrm{NN}}$. (f) The $m(K_S^0{K}^{+}{\pi }^{-})$ distribution of the data with the step-1 fit function overlaid.

Figure 3

Distributions of (a),(c),(e) $m(K_S^0{K}^{+}{\pi }^{-})$ and (b),(d),(f) $m(K_S^0{K}^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})$ with the step-2 fit PDF overlaid for the fit regions of the (a),(b) ${\chi }_{c2}(1P)$, (c),(d) ${\eta }_c(2S)$, and (e),(f) $X(3872)$, $X(3915)$ and ${\chi }_{c2}(2P)$. The vertical dashed lines in (f) indicate the peak mass positions of the $X(3872)$, $X(3915)$, and ${\chi }_{c2}(2P)$ [22].