First Observation of $D^{0(+)}\to \bar Kωe^+ν_e$ and Determination of the Branching Fraction of $\bar K_1(1270)\to \bar K ω$

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 $D^0\to K^-ωe^+ν_e$ and $D^+\to K_S^0ωe^+ν_e$ with significances of $8.0σ$ and $5.8σ$, respectively, including systematic uncertainties. Their decay branching fractions are measured to be ${\cal B}(D^0\to K^-ωe^+ν_e)=(9.3^{+2.1}_{-1.9}\pm 0.7)\times10^{-5}$ and ${\cal B}(D^+\to K_S^0ωe^+ν_e)=(6.6^{+2.0}_{-1.8}\pm 0.6)\times10^{-5}$. Combining with the latest measurements of $D^{0(+)}\to K^-π^+π^{-(0)} e^+ν_e$ and assuming $\bar{K}_1(1270)$ to be the sole mediating resonance in all processes, the branching ratios are determined to be $\frac{Γ(K_1(1270)^-\to K^-π^+π^-)}{Γ(K_1(1270)^-\to K^-ω)} = 3.4^{+0.8}_{-0.7} \pm 0.3$ and $\frac{Γ(\bar{K}_1(1270)^0\to K^-π^+π^0)}{Γ(\bar{K}_1(1270)^0\to \bar{K}^0ω)} = 9.6^{+3.0}_{-2.7} \pm 0.8$. The combined branching fraction is determined to be $\mathcal B(\bar{K}_1(1270)\to \bar{K}ω) = (7.5\pm 1.3 \pm 0.5)\%$, which is the most precise measurement from a collider experiment. The first uncertainties are statistical, and the second are systematic.