Study of $K_S^0$-$K_L^0$ asymmetry in the decays $D^0\to K_S^0\omega$ and $D^0\to K_L^0\omega$

Based on $e^{+}{e}^{-}$ annihilation data corresponding to an integrated luminosity of 7.93~$f{b}^{-1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider, the absolute branching fractions of the decays $D^0\to K_S^0\omega$ and $D^0\to K_L^0\omega$ are measured to be $(11.79\pm 0.19\pm 0.26\pm 0.47)\times {10}^{-3}$ and ($10.84\pm 0.14\pm 0.23\pm 0.44)\times {10}^{-3}$, respectively. The $K_S^0-K_L^0$ branching-fraction asymmetry of these two decays is $R(D^0,K_{S,L}^0\omega )=\frac{\mathcal{B}(D^0\to K_S^0\omega )-\mathcal{B}(D^0\to K_L^0\omega )}{\mathcal{B}(D^0\to K_S^0\omega )+\mathcal{B}(D^0\to K_L^0\omega )}=(4.2\pm 1.0\pm 0.9\pm 2.8)\mathrm{\%}$. Here, the first uncertainties are statistical, the second systematic, and the third arise from the interference between $D^0\to K_{S,L}^0\omega$ and the non-resonant $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0{K}_{S,L}^0$ processes.