Measurement of branching fractions of ψ(3686)→ϕη′, ϕf1(1285) and ϕη(1405)

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Abstract

Using a sample of $448.1\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\ensuremath{\psi}(3686)$ events collected with the BESIII detector, we perform a study of the decay $\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$. The branching fraction of $\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\eta}}^{\ensuremath{'}}$ is determined to be $(1.51\ifmmode\pm\else\textpm\fi{}0.16\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, which is consistent with the previous measurement but with significantly improved precision. The resonances ${f}_{1}(1285)$ and $\ensuremath{\eta}(1405)$ are clearly observed in the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$ mass spectrum with statistical significances of $18\ensuremath{\sigma}$ and $9.7\ensuremath{\sigma}$, respectively. The corresponding product branching fractions are measured to be $\mathcal{B}(\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\phi}{f}_{1}(1285)$, ${f}_{1}(1285)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta})=(1.03\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $\mathcal{B}(\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\eta}(1405)$, $\ensuremath{\eta}(1405)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta})=(8.46\ifmmode\pm\else\textpm\fi{}1.37\ifmmode\pm\else\textpm\fi{}0.92)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. These results are used to test the perturbative QCD ``12% rule.''

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