Partial Wave Analysis of $J/\ddot{I}ˆ\to {\hat{I}}^3{\hat{I}}^3\ddot{I}•$

Abstract

Using a sample of $(10087\pm 44)\times 10^6$ $J/\ddot{I}ˆ$ events collected by the BESIII detector at the BEPCII collider, a partial-wave analysis of the decay ${\hat{I}}^3{\hat{I}}^3\ddot{I}•$ is performed to investigate the intermediate resonances in $J/ψ\rightarrowγR, R\arγϕ$. Resonances including $f_1(1285)$, $\hat{I}\cdot (1405)$, $f_1(1420)$, $f_1(1510)$, $f_2(1525)$, $X(1835)$, $f_2(1950)$, $f_2(2010)$, $f_0(2200)$ and $\hat{I}{\cdot }_c$ have been detected with statistical significance greater than 5$\ddot{I}ƒ$. The product branching fractions $\mathcal{B}(J/ψ\rightarrowγR, R\ar γϕ)$ are reported, and the resonance parameters of $\hat{I}\cdot (1405)$ and $X(1835)$ have been precisely determined. It is more probable that $\hat{I}\cdot (1405)$ and $X(1835)$ act as the first - and second - excited states of $\hat{I}{\cdot }^{\prime }$, respectively. The observation of $\hat{I}{\cdot }_c\to {\hat{I}}^3\ddot{I}•$ holds great significance for the in depth study of charmonium properties. No evidence of $\hat{I}\cdot (1295)$, $\hat{I}{\cdot }_1(1855)$ or X(2370) is found. The measured upper limits of relevant BF products do not conflict with theoretical expectations for X(2370) as a pseudoscalar glueball and $\hat{I}{\cdot }_1(1855)$ as a hybrid state.