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Using $2.93~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at acenter-of-mass energy $\sqrt{s}=3.773$ GeV with the BESIII detector operatingat the BEPCII collider, we search for the semileptonic $D^{0(+)}$ decays into a$b_1(1235)^{-(0)}$ axial-vector meson for the first time. No significant signalis observed for either charge combination. The upper limits on the productbranching fractions are ${\mathcal B}_{D^0\to b_1(1235)^- e^+\nu_e}\cdot{\mathcal B}_{b_1(1235)^-\to \omega\pi^-}<1.12\times 10^{-4}$ and ${\mathcalB}_{D^+\to b_1(1235)^0 e^+\nu_e}\cdot {\mathcal B}_{b_1(1235)^0\to\omega\pi^0}<1.75\times 10^{-4}$ at the 90\% confidence level.

Search for the semileptonic decay $D^{0(+)}\to b_1(1235)^{-(0)} e^+\nu_e$