First study of ηc(1S), η(1760) and X(1835) production via η′π+π− final states in two-photon collisions

The invariant mass spectrum of the ${\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ final state produced in two-photon collisions is obtained using a $673\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data sample collected in the vicinity of the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. We observe a clear signal of the ${\ensuremath{\eta}}_{c}(1S)$ and measure its mass and width to be $M({\ensuremath{\eta}}_{c}(1S))=(2982.7\ifmmode\pm\else\textpm\fi{}1.8(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.2(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.3(\mathrm{\text{model}}))\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and $\ensuremath{\Gamma}({\ensuremath{\eta}}_{c}(1S))=({37.8}_{\ensuremath{-}5.3}^{+5.8}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.8(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}1.4(\mathrm{\text{model}}))\text{ }\text{ }\mathrm{MeV}/{c}^{2}$. The third error is an uncertainty due to possible interference between the ${\ensuremath{\eta}}_{c}(1S)$ and a nonresonant component. We also report the first evidence for $\ensuremath{\eta}(1760)$ decay to ${\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$; we find two solutions for its parameters, depending on the inclusion or not of the $X(1835)$, whose existence is of marginal significance in our data. From a fit to the mass spectrum using coherent $X(1835)$ and $\ensuremath{\eta}(1760)$ resonant amplitudes, we set a 90% confidence level upper limit on the product ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}\ensuremath{\gamma}}\mathcal{B}({\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ for the $X(1835)$.