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~$fb^{-1}$ 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 $R(D^0,K_{S,L}^{0} \omega) = \frac{\mathcal{B}(D^0 \to K_{S}^{0} \omega) - \mathcal{B}(D^0 \to K_{L}^{0}\omega )}{\mathcal{B}(D^0 \to K_{S}^{0} \omega) + \mathcal{B}(D^0 \to K_{L}^{0} \omega)} =(4.2 \pm 1.0 \pm 0.9 \pm 2.8)\%$. 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.