Study of $\phi\to K\bar{K}$ and $K_{S}^{0}-K_{L}^{0}$ Asymmetry in the Amplitude Analysis of $D_{s}^{+} \to K_{S}^{0}K_{L}^{0}\pi^{+}$ Decays

Abstract

Using $e^+e^-$ annihilation data corresponding to a total integrated luminosity of 7.33 $\rm fb^{-1}$ 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 $D_{s}^{+} \to K_{S}^{0}K_{L}^{0}\pi^{+}$. The branching fraction of $D_{s}^{+} \to K_{S}^{0}K_{L}^{0}\pi^{+}$ is determined to be $(1.86\pm0.06_{\rm stat}\pm0.03_{\rm syst})\%$. Combining the $\mathcal{B}[D_{s}^{+} \to \phi(\to K_{S}^0K_{L}^0) \pi^+]$ obtained in this work and the world average of $\mathcal{B}[D_{s}^{+} \to \phi(\to K^+K^-) \pi^+]$, we measure the relative branching fraction $\mathcal{B}(\phi \to K_S^0K_L^0)/\mathcal{B}(\phi \to K^+K^-)$=($0.593 \pm 0.023_{\rm stat} \pm 0.014_{\rm syst} \pm 0.016_{\phi\pi}$), where the third error is due to the uncertainty of the $\mathcal{B}(D_s^+ \to \phi \pi^+,\phi \to K^+K^-)$. Our result deviates from the Particle Data Group value by more than 3$\sigma$. Furthermore, the asymmetry of the branching fractions of $D^+_s\to K_{S}^0K^{*}(892)^{+}$ and $D^+_s\to K_{L}^0K^{*}(892)^{+}$, $\frac{\mathcal{B}[D_{s}^{+} \to K_{S}^0K^{*}(892)^{+}]-\mathcal{B}[D_{s}^{+} \to K_{L}^0K^{*}(892)^{+}]}{\mathcal{B}[D_{s}^{+} \to K_{S}^0K^{*}(892)^{+}]+\mathcal{B}[D_{s}^{+} \to K_{L}^0K^{*}(892)^{+}]}$, is determined to be $(-14.5\pm 5.1_{\rm stat}\pm 1.8_{\rm syst})\%$.