Observation of ${D}^{0}\to {K}_{1}\left(1270{\right)}^{-}{e}^{+}{\nu }_{e}$

Using $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data taken with the BESIII detector at a center-of-mass energy of 3.773 GeV, the observation of the ${D}^{0}\to {K}_{1}\left(1270{\right)}^{-}{e}^{+}{\nu }_{e}$ semileptonic decay is presented. The statistical significance of the decay ${D}^{0}\to {K}_{1}\left(1270{\right)}^{-}{e}^{+}{\nu }_{e}$ is greater than $10\sigma $. The branching fraction of ${D}^{0}\to {K}_{1}\left(1270{\right)}^{-}{e}^{+}{\nu }_{e}$ is measured to be $\left(1.09±0.1{3}_{-0.16}^{+0.09}±0.12\right)×{10}^{-3}$. Here, the first uncertainty is statistical, the second is systematic, and the third originates from the assumed branching fraction of ${K}_{1}\left(1270{\right)}^{-}\to {K}^{-}{\pi }^{+}{\pi }^{-}$. The fraction of longitudinal polarization in ${D}^{0}\to {K}_{1}\left(1270{\right)}^{-}{e}^{+}{\nu }_{e}$ is determined for the first time to be $0.50±0.1{9}_{\mathrm{stat}}±0.0{8}_{\mathrm{syst}}$.