Study of $ \varphi \to K\overline{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

Using $ {e}^{+}{e}^{-}$ annihilation data corresponding to a total integrated luminosity of $ 7.33\text{}\text{}{\mathrm{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\pm 0.0{6}_{\mathrm{stat}}\pm 0.0{3}_{\mathrm{syst}})\%$. Combining the $ \mathcal{B}[{D}_{s}^{+}\to \varphi (\to {K}_{S}^{0}{K}_{L}^{0}){\pi }^{+}]$ obtained in this Letter and the world average of $ \mathcal{B}[{D}_{s}^{+}\to \varphi (\to {K}^{+}{K}^{-}){\pi }^{+}]$, we measure the relative branching fraction $ \mathcal{B}(\varphi \to {K}_{S}^{0}{K}_{L}^{0})/\mathcal{B}(\varphi \to {K}^{+}{K}^{-})=(0.593\pm 0.02{3}_{\mathrm{stat}}\pm \phantom{\rule{0ex}{0ex}}0.01{4}_{\mathrm{syst}}\pm 0.01{6}_{\varphi \pi })$, where the third error is due to the uncertainty of the $ \mathcal{B}({D}_{s}^{+}\to \varphi {\pi }^{+},\varphi \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}^{0}{K}^{*}(892{)}^{+}$ and $ {D}_{s}^{+}\to {K}_{L}^{0}{K}^{*}(892{)}^{+}$, $ \mathbf{(}\{\mathcal{B}[{D}_{s}^{+}\to {K}_{S}^{0}{K}^{*}(892{)}^{+}]-\phantom{\rule{0ex}{0ex}}\mathcal{B}[{D}_{s}^{+}\to {K}_{L}^{0}{K}^{*}(892{)}^{+}]\}/\{\mathcal{B}[{D}_{s}^{+}\to {K}_{S}^{0}{K}^{*}(892{)}^{+}]+\mathcal{B}[{D}_{s}^{+}\to {K}_{L}^{0}{K}^{*}(892{)}^{+}]\}\mathbf{)}$, is determined to be $ (-14.5\pm {5.1}_{\mathrm{stat}}\pm {1.8}_{\mathrm{syst}})\%$.