Search for the decays $X(3872)\to K_{S}^{0}K^{\pm}\pi^{\mp}$ and $K^*(892)\bar{K}$ 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 $X(3872) \to K_{S}^{0}K^{\pm}\pi^{\mp}$ and $K^*(892)\bar{K}$, where the $X(3872)$ is produced via the radiative process $e^+e^- \to \gamma X(3872)$. No significant signal is observed. We set upper limits on the relative branching fractions $\mathcal{B}[X(3872)\to K_S K^{\pm} \pi^{\mp}]/\mathcal{B}[X(3872)\to\pi^+\pi^- J/\psi] <0.07$ and $\mathcal{B}[X(3872)\to K^* (892)\bar{K}]/\mathcal{B}[X(3872)\to \pi^+\pi^- J/\psi] <0.10$ at the 90$\%$ confidence level. Additionally, upper limits on the product of the cross section $\sigma[e^+e^-\to\gamma X(3872)]$ and the branching fractions $\mathcal{B}[X(3872)\to K_{S}^{0}K^{\pm}\pi^{\mp}]$ and $\mathcal{B}[X(3872)\to K^*(892)\bar{K}]$ are reported at each energy point. In all cases, $K^*(892)\bar{K}$ refers to the sum of the modes $K^*(892)^+K^{-}+\text{c.c.}$ and $K^*(892)^0\bar{K}^0+\text{c.c.}$, where c.c. denotes the corresponding charge-conjugate modes.