Search for the semileptonic decay ${D}^{0\left(+\right)}\to {b}_{1}\left(1235{\right)}^{-\left(0\right)}{e}^{+}{\nu }_{e}$

Using $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy $\sqrt{s}=3.773\text{}\text{}\mathrm{GeV}$ with the BESIII detector operating at the BEPCII collider, we search for the semileptonic ${D}^{0\left(+\right)}$ decays into a ${b}_{1}\left(1235{\right)}^{-\left(0\right)}$ axial-vector meson for the first time. No significant signal is observed for either charge combination. The upper limits on the product branching fractions are ${B}_{{D}^{0}\to {b}_{1}\left(1235{\right)}^{-}{e}^{+}{\nu }_{e}}·{B}_{{b}_{1}\left(1235{\right)}^{-}\to \omega {\pi }^{-}}<\phantom{\rule{0ex}{0ex}}1.12×{10}^{-4}$ and ${B}_{{D}^{+}\to {b}_{1}\left(1235{\right)}^{0}{e}^{+}{\nu }_{e}}·{B}_{{b}_{1}\left(1235{\right)}^{0}\to \omega {\pi }^{0}}<1.75×{10}^{-4}$ at the 90% confidence level.