First Observation of $D^{0(+)}\to \bar{K}\omega e^{+}{\nu }_e$ and Determination of the Branching Fraction of ${\bar{K}}_1(1270)\to \bar{K}\omega$

Using 20.3~fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector, we report the first observation of the semileptonic decays $D^0\to K^{-}\omega e^{+}{\nu }_e$ and $D^{+}\to K_S^0\omega e^{+}{\nu }_e$ with significances of $8.0\sigma$ and $5.8\sigma$, respectively, including systematic uncertainties. Their decay branching fractions are measured to be $\mathcal{B}(D^0\to K^{-}\omega e^{+}{\nu }_e)=(9.3_{-1.9}^{+2.1}\pm 0.7)\times {10}^{-5}$ and $\mathcal{B}(D^{+}\to K_S^0\omega e^{+}{\nu }_e)=(6.6_{-1.8}^{+2.0}\pm 0.6)\times {10}^{-5}$. Combining with the latest measurements of $D^{0(+)}\to K^{-}{\pi }^{+}{\pi }^{-(0)}{e}^{+}{\nu }_e$ and assuming ${\bar{K}}_1(1270)$ to be the sole mediating resonance in all processes, the branching ratios are determined to be $\frac{\mathrm{\Gamma }(K_1(1270{)}^{-}\to K^{-}{\pi }^{+}{\pi }^{-})}{\mathrm{\Gamma }(K_1(1270{)}^{-}\to K^{-}\omega )}=3.4_{-0.7}^{+0.8}\pm 0.3$ and $\frac{\mathrm{\Gamma }({\bar{K}}_1(1270{)}^0\to K^{-}{\pi }^{+}{\pi }^0)}{\mathrm{\Gamma }({\bar{K}}_1(1270{)}^0\to {\bar{K}}^0\omega )}=9.6_{-2.7}^{+3.0}\pm 0.8$. The combined branching fraction is determined to be $\mathcal{B}({\bar{K}}_1(1270)\to \bar{K}\omega )=(7.5\pm 1.3\pm 0.5)\mathrm{\%}$, which is the most precise measurement from a collider experiment. The first uncertainties are statistical, and the second are systematic.