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We report the first measurements of the absolute branching fractions of$D^0\to K_L^0\phi$, $D^0\to K_L^0\eta$, $D^0\to K_L^0\omega$, and $D^0\toK_L^0\eta^{\prime}$, obtained by analyzing $2.93\,\rm fb^{-1}$ of $e^+e^-$collision data taken at a center-of-mass energy of 3.773 GeV with the BESIIIdetector. Taking the world averages of the branching fractions of $D^0\toK_S^0\phi$, $D^0\to K_S^0\eta$, $D^0\to K_S^0\omega$, and $D^0\toK_S^0\eta^{\prime}$, the $K_S^0$-$K_L^0$ asymmetry $\mathcal{R}(D^0)$ in thesedecay modes are obtained. The CP asymmetries in these decays are alsodetermined. No significant $CP$ violation is observed.

Measurements of Absolute Branching Fractions of $D^0\to K_L^0\phi$, $K_L^0\eta$, $K_L^0\omega$, and $K_L^0\eta^{\prime}$