Measurement of the Electromagnetic Transition Form-factors in the decays $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{l}^{+}{l}^{-}$

Abstract

With a sample of $(10087\pm 44)\times 10^6$ $J/\ddot{I}ˆ$ events accumulated with the BESIII detector, we analyze the decays $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{l}^{+}{l}^{-}(l=e,$ $\hat{I}¼)$ via the process $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }^{\prime }$. The branching fractions are measured to be $\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{e}^{+}{e}^{-})=(2.45\pm 0.02(stat.)\pm 0.08(syst.))\times 10^{-3}$ and $\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{¼}^{-})=(2.16\pm 0.12(stat.)\pm 0.06(syst.))\times 10^{-5}$, and the ratio is $\frac{\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{e}^{+}{e}^{-})}{\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{¼}^{-})}=113.4\pm 0.9(stat.)\pm 3.7(syst.)$. In addition, by combining the $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{e}^{+}{e}^{-}$ and $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ decays, the slope parameter of the electromagnetic transition form factor is measured to be $b_{\hat{I}{\cdot }^{\prime }}=1.30\pm 0.19(\mathrm{GeV}/c^2{)}^{-2}$, which is consistent with previous measurements from BESIII and theoretical predictions from the VMD model. The asymmetry in the angle between the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $l^{+}{l}^{-}$ decay planes, which has the potential to reveal the $CP$-violation originating from an unconventional electric dipole transition, is also investigated. The asymmetry parameters are determined to be ${\mathcal{A}}_{CP}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{e}^{+}{e}^{-})=(-0.21\pm 0.73(stat.)\pm 0.01(syst.))\%$ and ${\mathcal{A}}_{CP}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{¼}^{-})=(0.62\pm 4.71(stat.)\pm 0.08(syst.))\%$, implying that no evidence of $CP$-violation is observed at the present statistics. Finally, an axion-like particle is searched for via the decay $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}a,a\to e^{+}{e}^{-}$, and upper limits of the branching fractions are presented for the mass assumptions of the axion-like particle in the range of $0-500\mathrm{MeV}/c^2$.