Measurement of ${\eta }_c\left(1S\right)$ , ${\eta }_c\left(2S\right)$ , and nonresonant ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ production via two-photon collisions

We report the measurement of $\gamma \gamma \to {\eta }_c\left(1S\right),{\eta }_c\left(2S\right)\to {\eta }^{\text{'}}{\pi }^{+}{\pi }^{-}$ with ${\eta }^{\text{'}}$ decays to $\gamma \rho$ and $\eta {\pi }^{+}{\pi }^{-}$ using $941{\mathrm{fb}}^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The ${\eta }_c\left(1S\right)$ mass and width are measured to be $M=\left[2984.6\pm 0.7\right(\mathrm{stat})\pm 2.2(\mathrm{syst})\pm 0.3(\mathrm{model}\left)\right]\mathrm{MeV}/c^2$ and $\Gamma =\left[30.8_{-2.2}^{+2.3}\right(\mathrm{stat})\pm 2.5(\mathrm{syst})\pm 1.4(\mathrm{model}\left)\right]\mathrm{MeV}$, respectively. First observation of ${\eta }_c\left(2S\right)\to {\eta }^{\text{'}}{\pi }^{+}{\pi }^{-}$ with a significance of $5.5\sigma$ including systematic error is obtained, and the ${\eta }_c\left(2S\right)$ mass is measured to be $M=\left[3635.1\pm 3.7\right(\mathrm{stat})\pm 2.9(\mathrm{syst})\pm 0.4(\mathrm{model}\left)\right]\mathrm{MeV}/c^2$. The products of the two-photon decay width and branching fraction ($B$) of decays to ${\eta }^{\text{'}}{\pi }^{+}{\pi }^{-}$ are determined to be ${\Gamma }_{\gamma \gamma }$${\Gamma }_{\gamma \gamma }B=[65.4\pm 2.6(\mathrm{stat}\left)\pm 7.8\right(\mathrm{syst}\left)\right]\mathrm{eV}$ for ${\eta }_c\left(1S\right)$ and $\left[{5.6}_{-1.1}^{+1.2}\right(\mathrm{stat})\pm 1.1(\mathrm{syst}\left)\right]\mathrm{eV}$ for ${\eta }_c\left(2S\right)$. The cross sections for $\gamma \gamma \to {\eta }^{\text{'}}{\pi }^{+}{\pi }^{-}$ and ${\eta }^{\text{'}}{f}_2\left(1270\right)$ are measured for the first time.