Search for the decays $X(3872)\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp }$ and $K^{\ast }(892)\bar{K}$ at BESIII

Abstract

Using a 10.9 fb${}^{-1}$ data sample collected by the BESIII detector at center-of-mass energies from 4.16 to 4.34 GeV, we search for the charmless decays $X(3872)\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp }$ and $K^{\ast }(892)\bar{K}$, where the $X(3872)$ is produced via the radiative process $e^{+}{e}^{-}\to {\hat{I}}^{3}X(3872)$. No significant signal is observed. We set upper limits on the relative branching fractions $\mathcal{B}[X(3872)\to K_S{K}^{\pm }\ddot{I}{€}^{\mp }]/\mathcal{B}[X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}J/\ddot{I}ˆ]<0.07$ and $\mathcal{B}[X(3872)\to K^{\ast }(892)\bar{K}]/\mathcal{B}[X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}J/\ddot{I}ˆ]<0.10$ at the 90$\%$ confidence level. Additionally, upper limits on the product of the cross section $\ddot{I}ƒ[e^{+}{e}^{-}\to {\hat{I}}^{3}X(3872)]$ and the branching fractions $\mathcal{B}[X(3872)\to K_S^0{K}^{\pm }\ddot{I}{€}^{\mp }]$ and $\mathcal{B}[X(3872)\to K^{\ast }(892)\bar{K}]$ are reported at each energy point. In all cases, $K^{\ast }(892)\bar{K}$ refers to the sum of the modes $K^{\ast }(892{)}^{+}{K}^{-}+\text{c.c.}$ and $K^{\ast }(892{)}^0{\bar{K}}^0+\text{c.c.}$, where c.c. denotes the corresponding charge-conjugate modes.

11 pages, 1 figure