Search for the decays X(3872) → K0SKπ∓ and K(892)K¯ at BESIII

Using a $10.9~\mathrm{fb}^{-1}$ data sample collected by the BESIII detector at center-of-mass energies from $4.16$ to $4.34~\mathrm{GeV}$, we search for the charmless decays $X(3872)\to K_S^0K^\pm\pi^\mp$ and $X(3872)\to K(892)\bar{K}$, 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 $$\frac{\mathcal{B}[X(3872)\to K_S^0K^\pm\pi^\mp]}{\mathcal{B}[X(3872)\to\pi^+\pi^-J/\psi]} < 0.07$$ and $$\frac{\mathcal{B}[X(3872)\to K(892)\bar{K}]}{\mathcal{B}[X(3872)\to\pi^+\pi^-J/\psi]} < 0.10$$ 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 $\mathcal{B}[X(3872)\to K_S^0K^\pm\pi^\mp]$ 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 $K(892)^+K^- + \mathrm{c.c.}$ and $K(892)^0\bar{K}^0 + \mathrm{c.c.}$, where $\mathrm{c.c.}$ denotes the corresponding charge-conjugate modes.