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

Using $2.93~mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy $sqrt{s}=3.773$ GeV with the BESIII detector operating at 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 signal is observed for either charge combination. The upper limits on the product branching fractions are ${mathcal B}_{D^0to b_1(1235)^- e^+ u_e}cdot {mathcal B}_{b_1(1235)^-to omegapi^-}<1.12times 10^{-4}$ and ${mathcal B}_{D^+to b_1(1235)^0 e^+ u_e}cdot {mathcal B}_{b_1(1235)^0to omegapi^0}<1.75times 10^{-4}$ at the 90% confidence level.