Search for the radiative decays $D^0\to \gamma {\bar{K}}_1(1270{)}^0$ and $D^{+}\to \gamma K_1(1270{)}^{+}$

A search for the radiative decays $D^0\to \gamma {\bar{K}}_1(1270{)}^0$ and $D^{+}\to \gamma K_1(1270{)}^{+}$ is conducted using $20.3{\mathrm{f}\mathrm{b}}^{-1}$ 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 $D^0\to \gamma {\bar{K}}_1(1270{)}^0$ and $D^{+}\to \gamma K_1(1270{)}^{+}$ at 90% confidence level are determined to be $7.7\times {10}^{-4}$ and $3.9\times {10}^{-5}$, respectively. This represents the first test of the Vector Meson Dominance mechanism in the radiative decays of charmed mesons to axial-vector mesons.