Search for the radiative transitions $\ddot{I}ˆ(3770)\to {\hat{I}}^3\hat{I}{\cdot }_c$ and ${\hat{I}}^3\hat{I}{\cdot }_c(2S)$

Abstract

By using a 2.92 fb${}^{-1}$ data sample taken at $\sqrt{s}=3.773$ GeV with the BESIII detector operating at the BEPCII collider, we search for the radiative transitions $\ddot{I}ˆ(3770)\to {\hat{I}}^3\hat{I}{\cdot }_c$ and ${\hat{I}}^3\hat{I}{\cdot }_c(2S)$ through the hadronic decays $\hat{I}{\cdot }_c(\hat{I}{\cdot }_c(2S))\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp }$. No significant excess of signal events above background is observed. We set upper limits at a 90% confidence level for the product branching fractions to be $\mathcal{B}(\ddot{I}ˆ(3770)\to {\hat{I}}^3\hat{I}{\cdot }_c)\times \mathcal{B}(\hat{I}{\cdot }_c\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp })<1.6\times 10^{-5}$ and $\mathcal{B}(\ddot{I}ˆ(3770)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S))\times \mathcal{B}(\hat{I}{\cdot }_c(2S)\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp })<5.6\times 10^{-6}$. Combining our result with world-average values of $\mathcal{B}(\hat{I}{\cdot }_c(\hat{I}{\cdot }_c(2S))\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp })$, we find the branching fractions $\mathcal{B}(\ddot{I}ˆ(3770)\to {\hat{I}}^3\hat{I}{\cdot }_c)<6.8\times 10^{-4}$ and $\mathcal{B}(\ddot{I}ˆ(3770)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S))<2.0\times 10^{-3}$ at a 90% confidence level.

10 pages, 4 figures