Improved measurements of the Dalitz decays $\hat{I}\cdot /\hat{I}{\cdot }^{\prime }\to {\hat{I}}^3{e}^{+}{e}^{-}$

Abstract

Based on a data sample of 10 billion $J/\ddot{I}ˆ$ events collected with the BESIII detector, improved measurements of the Dalitz decays $\hat{I}\cdot /\hat{I}{\cdot }^{\prime }\to {\hat{I}}^3{e}^{+}{e}^{-}$ are performed, where the $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$ are produced through the radiative decays $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot /\hat{I}{\cdot }^{\prime }$. The branching fractions of $\hat{I}\cdot \to {\hat{I}}^3{e}^{+}{e}^{-}$ and $\hat{I}{\cdot }^{\prime }\to {\hat{I}}^3{e}^{+}{e}^{-}$ are measured to be $(7.07\pm 0.05\pm 0.23)\times 10^{-3}$ and $(4.83\pm 0.07\pm 0.14)\times 10^{-4}$, respectively. Within the single pole model, the parameter of electromagnetic transition form factor for $\hat{I}\cdot \to {\hat{I}}^3{e}^{+}{e}^{-}$ is determined to be $\hat{I}{›}_{\hat{I}}\cdot =(0.749\pm 0.027\pm 0.007)\mathrm{GeV}/c^2$. Within the multi-pole model, we extract the electromagnetic transition form factors for $\hat{I}{\cdot }^{\prime }\to {\hat{I}}^3{e}^{+}{e}^{-}$ to be $\hat{I}{›}_{\hat{I}{\cdot }^{\prime }}=(0.802\pm 0.007\pm 0.008)\mathrm{GeV}/c^2$ and ${\hat{I}}_{\hat{I}{\cdot }^{\prime }}^3=(0.113\pm 0.010\pm 0.002)\mathrm{GeV}/c^2$. The results are consistent with both theoretical predictions and previous measurements. The characteristic sizes of the interaction regions for the $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$ are calculated to be $(0.645\pm 0.023\pm 0.007)\mathrm{fm}$ and $(0.596\pm 0.005\pm 0.006)\mathrm{fm}$, respectively. In addition, we search for the dark photon in $\hat{I}\cdot /\hat{I}{\cdot }^{\prime }\to {\hat{I}}^3{e}^{+}{e}^{-}$, and the upper limits of the branching fractions as a function of the dark photon are given at 90\% confidence level.