Search for the isospin-violating decays $\ddot{\mathbf{I}}{‡}_{\mathbf{cJ}}\to \hat{\mathbf{I}}›\overline{\hat{\mathbf{I}}}{\pounds }^0+\mathbf{c}.\mathbf{c}.$ and $\hat{\mathbf{I}}{\cdot }_{\mathbf{c}}\to \hat{\mathbf{I}}›\overline{\hat{\mathbf{I}}}{\pounds }^0+\mathbf{c}.\mathbf{c}.$

Abstract

Using a sample of $(2712.4\pm 14.3)\times 10^6$~$\ddot{I}ˆ(3686)$ events collected with the BESIII detector, we perform a search for the isospin-violating decays $\ddot{I}{‡}_{cJ}\to \hat{I}›\bar{\hat{I}}{\pounds }^0+c.c.(J=0,1,2)$ and $\hat{I}{\cdot }_c\to \hat{I}›\bar{\hat{I}}{\pounds }^0+c.c.$ No significant signal for $\ddot{I}{‡}_{cJ}$ or $\hat{I}{\cdot }_c$ is observed in the $\hat{I}›\bar{\hat{I}}{\pounds }^0$ invariant mass distribution. The upper limits on the branching fractions at the 90\% confidence level are set to be $\mathcal{B}$($\ddot{I}{‡}_{c0}\to \hat{I}›\bar{\hat{I}}{\pounds }^0+c.c.$)$<1.5\times 10^{-6}$, $\mathcal{B}$($\ddot{I}{‡}_{c1}\to \hat{I}›\bar{\hat{I}}{\pounds }^0+c.c.$)$<1.6\times 10^{-6}$, $\mathcal{B}$($\ddot{I}{‡}_{c2}\to \hat{I}›\bar{\hat{I}}{\pounds }^0+c.c.$)$<1.7\times 10^{-6}$ and $\mathcal{B}$($\hat{I}{\cdot }_c\to \hat{I}›\bar{\hat{I}}{\pounds }^0+c.c.$)$<6.2\times 10^{-5}$ for the first time.