Measurement of the Branching Fraction of \boldmath{$\ddot{I}ˆ(2S)\to {\hat{I}}^3\ddot{I}{€}^0$}

Abstract

Based on $(2712.4\pm 14.1)\times 10^6\ddot{I}ˆ(2S)$ events, 7.9 fb${}^{-1}$ $\ddot{I}ˆ(3773)$ data, and 0.8 fb${}^{-1}$ off-resonance data samples collected with the BESIII detector, we measure the branching fraction of $\ddot{I}ˆ(2S)\to {\hat{I}}^3\ddot{I}{€}^0$ and $e^{+}{e}^{-}\to {\hat{I}}^3\ddot{I}{€}^0$ form factor at momentum transfers $Q^2\sim 13$ GeV${}^2$. The $e^{+}{e}^{-}\to {\hat{I}}^3\ddot{I}{€}^0$ cross section is fitted with considering the interference between the $\ddot{I}ˆ(2S)$ and continuum amplitudes and two solutions are found, $\mathcal{B}=3.74\times 10^{-7}$ with $\ddot{I}•=3.93$ rad and $\mathcal{B}=7.87\times 10^{-7}$ with $\ddot{I}•=2.08$ rad. Here, $\mathcal{B}$ is the branching fraction of $\ddot{I}ˆ(2S)\to {\hat{I}}^3\ddot{I}{€}^0$ and $\ddot{I}•$ is the relative phase angle between the $\ddot{I}ˆ(2S)$ and continuum amplitudes. Due to insufficient off-resonance data, the branching fraction $\mathcal{B}(\ddot{I}ˆ(2S)\to {\hat{I}}^3\ddot{I}{€}^0)$ is determined to be in the range $[2.7,9.7]\times 10^{-7}$ within one standard deviation of the contour region.