Search for the radiative decays $D^0\to γ\bar K_1(1270)^0$ and $D^+\to γK_1(1270)^+$

A search for the radiative decays $D^0\to γ\bar K_1(1270)^0$ and $D^+\to γK_1(1270)^+$ is conducted using $20.3~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at the center-of-mass energy $\sqrt{s}=3.773$ GeV by the BESIII detector operating at the BEPCII collider. No significant signals are observed, and upper limits on the branching fractions of $D^0\to γ\bar K_1(1270)^0$ and $D^+\to γK_1(1270)^+$ at 90\% confidence level are determined to be $7.7\times10^{-4}$ and $3.9\times10^{-5}$, respectively. This represents the first test of the Vector Meson Dominance mechanism in the radiative decays of charmed mesons to axial-vector mesons.