We present the first systematic study of the radiative decays of charmed mesons using $2+1$-flavor clover fermion gauge ensembles generated by the CLQCD Collaboration. One of the ensembles is at the physical pion mass, and one has a fine lattice spacing $a\sim 0.05\mathrm{fm}$. We determine the coupling constants to be $g_{D^{*+}{D}^{+}\gamma }=-0.204(22){\mathrm{GeV}}^{-1}$, $g_{D^{*0}{D}^0\gamma }=1.73(37){\mathrm{GeV}}^{-1}$, and $g_{D_s^{*+}{D}_s^{+}\gamma }=-0.120(14){\mathrm{GeV}}^{-1}$, respectively. Compared with previous studies, our results demonstrate significant improvements in precision. In particular, we carefully estimate the systematic uncertainty arising from matrix element fits, momentum transfer extrapolations, and chiral and continuum limit extrapolations, which are included in the reported total uncertainties. These couplings yield the following predictions of decay widths: ${\mathrm{\Gamma }}_{D^{*+}\to D^{+}\gamma }=0.253(55)\mathrm{keV}$, ${\mathrm{\Gamma }}_{D^{*0}\to D^0\gamma }=18.2(7.8)\mathrm{keV}$, and ${\mathrm{\Gamma }}_{D_s^{*+}\to D_s^{+}\gamma }=0.094(22)\mathrm{keV}$. This work establishes first-principles results of the charmed meson radiative transitions and provides inputs for understanding the structure and properties of heavy-light mesons.

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• Lattice QCD