Study of the Magnetic Dipole Transition of $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }_c$ via $\hat{I}{\cdot }_c\to p\bar{p}$

Abstract

Using $(10.087\pm 0.044)\times 10^9$ $J/\ddot{I}ˆ$ events collected with the BESIII detector at the $e^{+}{e}^{-}$ BEPCII collider, we present the first amplitude analysis of $J/\ddot{I}ˆ\to {\hat{I}}^{3}p\bar{p}$ with the $p\bar{p}$ invariant mass in the $\hat{I}{\cdot }_c$ mass region $[2.70,3.05]$~GeV/$c^2$. The product branching fraction $\mathcal{B}(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }_c)\times \mathcal{B}(\hat{I}{\cdot }_c\to p\bar{p})$ is precisely determined to be $(2.11\pm 0.02_{\mathrm{stat}}\pm 0.07_{\mathrm{syst}})\times 10^{-5}$. Combining with the product branching fractions $\mathcal{B}(\hat{I}{\cdot }_c\to p\bar{p})\times \mathcal{B}(\hat{I}{\cdot }_c\to {\hat{I}}^3{\hat{I}}^3)$ and $\mathcal{B}(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }_c)\times \mathcal{B}(\hat{I}{\cdot }_c\to {\hat{I}}^3{\hat{I}}^3)$, the branching fractions of $\mathcal{B}(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }_c)$ and $\mathcal{B}(\hat{I}{\cdot }_c\to {\hat{I}}^3{\hat{I}}^3)$ are calculated to be $(2.29\pm 0.01_{\mathrm{stat}}\pm 0.04_{\mathrm{syst}}\pm 0.18_{\mathrm{opbf}})\%$ and $(2.28\pm 0.01_{\mathrm{stat}}\pm 0.04_{\mathrm{syst}}\pm 0.18_{\mathrm{opbf}})\times 10^{-4}$, respectively, which are consistent with the latest lattice quantum chromodynamics calculations. Here, opbf is the uncertainty from the other product branching fractions used in the calculation.

11 Pages, 3 figures, submit to PRL