Probing QCD dynamics and the standard model with $$ {D}_{(s)}^{+}\to {P}_1^{+}{P}_2^0\gamma $$ decays

We compute 10 radiative three-body decays of charged charmed mesons $$ {D}^{+}\to {P}_1^{+}{P}_2^0\gamma $$ D + → P 1 + P 2 0 γ and $$ {D}_s\to {P}_1^{+}{P}_2^0\gamma $$ D s → P 1 + P 2 0 γ , P1,2 = π, K, in leading order QCDF, HHχPT and the soft photon approximation. We work out decay distributions and asymmetries in the standard model and with new physics in the electromagnetic dipole operators. The forward-backward asymmetry is suitable to probe the QCD frameworks, in particular the s-channel dependent weak annihilation contributions in QCDF against the markedly different resonance structure in HHχPT. These studies can be performed with Cabibbo-favored modes Ds → π+π0γ, $$ {D}^{+}\to {\pi}^{+}{\overline{K}}^0\gamma $$ D + → π + K ¯ 0 γ and $$ {D}_s\to {K}^{+}{\overline{K}}^0\gamma $$ D s → K + K ¯ 0 γ with $$ \mathcal{O}\left({10}^{-4}-{10}^{-3}\right)\hbox{-} \mathrm{level} $$ O 10 − 4 − 10 − 3 ‐ level branching ratio, which are standard model-like and induced by different hadronic dynamics. Understanding of the latter can therefore be improved in a data-driven way and sharpens the interpretation of standard model tests. Singly Cabibbo-suppressed modes such as D+ → π+π0γ, Ds → π+K0γ, Ds → K+π0γ with branching ratios within ∼ 10−5–10−4 are sensitive to new physics that can be signalled in the forward-backward asymmetry and in the CP-asymmetry of the rate, ideally in the Dalitz region but also in single differential distributions. Results complement those with neutral D0→ P1P2γ decays.