Study of $\ddot{I}•\to K\bar{K}$ and $K_S^0-K_L^0$ Asymmetry in the Amplitude Analysis of $D_s^{+}\to K_S^0{K}_L^0\ddot{I}{€}^{+}$ Decays

Abstract

Using $e^{+}{e}^{-}$ annihilation data corresponding to a total integrated luminosity of 7.33 $\mathrm{f}{\mathrm{b}}^{-1}$ collected at center-of-mass energies between 4.128 and 4.226~GeV with the BESIII detector, we provide the first amplitude analysis and absolute branching fraction measurement of the hadronic decay $D_s^{+}\to K_S^0{K}_L^0\ddot{I}{€}^{+}$. The branching fraction of $D_s^{+}\to K_S^0{K}_L^0\ddot{I}{€}^{+}$ is determined to be $(1.86\pm 0.06_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}})\%$. Combining the $\mathcal{B}[D_s^{+}\to \ddot{I}•(\to K_S^0{K}_L^0)\ddot{I}{€}^{+}]$ obtained in this work and the world average of $\mathcal{B}[D_s^{+}\to \ddot{I}•(\to K^{+}{K}^{-})\ddot{I}{€}^{+}]$, we measure the relative branching fraction $\mathcal{B}(\ddot{I}•\to K_S^0{K}_L^0)/\mathcal{B}(\ddot{I}•\to K^{+}{K}^{-})$=($0.593\pm 0.023_{\mathrm{stat}}\pm 0.014_{\mathrm{syst}}\pm 0.016_{\ddot{I}•\ddot{I}€}$), where the third error is due to the uncertainty of the $\mathcal{B}(D_s^{+}\to \ddot{I}•\ddot{I}{€}^{+},\ddot{I}•\to K^{+}{K}^{-})$. Our result deviates from the Particle Data Group value by more than 3$\ddot{I}ƒ$. Furthermore, the asymmetry of the branching fractions of $D_s^{+}\to K_S^0{K}^{\ast }(892{)}^{+}$ and $D_s^{+}\to K_L^0{K}^{\ast }(892{)}^{+}$, $\frac{\mathcal{B}[D_s^{+}\to K_S^0{K}^{\ast }(892{)}^{+}]-\mathcal{B}[D_s^{+}\to K_L^0{K}^{\ast }(892{)}^{+}]}{\mathcal{B}[D_s^{+}\to K_S^0{K}^{\ast }(892{)}^{+}]+\mathcal{B}[D_s^{+}\to K_L^0{K}^{\ast }(892{)}^{+}]}$, is determined to be $(-14.5\pm 5.1_{\mathrm{stat}}\pm 1.8_{\mathrm{syst}})\%$.

11 pages, 4 figures