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We compute 10 radiative three-body decays of charged charmed mesons $D^+ \toP^+ P^0 \gamma$ and $D_s \to P^+ P^0 \gamma$, $P=\pi, K$, in leading orderQCDF, HH$\chi$PT and the soft photon approximation. We work out decaydistributions and asymmetries in the standard model and with new physics in theelectromagnetic dipole operators. The forward-backward asymmetry is suitable toprobe the QCD frameworks, in particular the $s$-channel dependent weakannihilation contributions in QCDF against the markedly different resonancestructure in HH$\chi$PT. These studies can be performed with Cabibbo-favoredmodes $D_s \to \pi^+ \pi^0 \gamma$, $D^+ \to \pi^+ \overline{K}^0 \gamma$ and$D_s \to K^+ \overline{K}^0 \gamma$ with ${\cal{O}}(10^{-4}-10^{-3})$-levelbranching ratio, which are standard model-like and induced by differenthadronic dynamics. Understanding of the latter can therefore be improved in adata-driven way and sharpens the interpretation of standard model tests. SinglyCabibbo-suppressed modes such as $ D^+ \to \pi^+ \pi^0 \gamma$, $D_s \to \pi^+K^0 \gamma$, $D_s \to K^+ \pi^0 \gamma$ with branching ratios within $\sim10^{-5}-10^{-4}$ are sensitive to new physics that can be signalled in theforward-backward asymmetry and in the CP-asymmetry of the rate, ideally in theDalitz region but also in single differential distributions. Results complementthose with neutral $D^0 \to PP \gamma$ decays.

Probing QCD dynamics and the standard model with $D_{(s)} \to P^+ P^0 \gamma$ decays