We study radiative charm decays $$D \rightarrow P_1 P_2 \gamma $$ D → P 1 P 2 γ , $$P_{1,2}=\pi ,K$$ P 1 , 2 = π , K in QCD factorization at leading order and within heavy hadron chiral perturbation theory. Branching ratios including resonance contributions are around $$\sim 10^{-3}$$ ∼ 10 - 3 for the Cabibbo-favored modes into $$K \pi \gamma $$ K π γ and $$\sim 10^{-5}$$ ∼ 10 - 5 for the singly Cabibbo-suppressed modes into $$\pi ^+ \pi ^- \gamma , K^+ K^- \gamma $$ π + π - γ , K + K - γ , and thus in reach of the flavor factories BES III and Belle II. Dalitz plots and forward–backward asymmetries reveal significant differences between the two QCD frameworks; such observables are therefore ideally suited for a data-driven identification of relevant decay mechanisms in the standard-model dominated $$D \rightarrow K \pi \gamma $$ D → K π γ decays. This increases the potential to probe new physics with the $$D \rightarrow \pi ^+ \pi ^- \gamma $$ D → π + π - γ and $$D \rightarrow K^+ K^- \gamma $$ D → K + K - γ decays, which are sensitive to enhanced dipole operators. CP asymmetries are useful to test the SM and look for new physics in neutral $$|\Delta C|=1$$ | Δ C | = 1 transitions. Cuts in the Dalitz plot enhance the sensitivity to new physics due to the presence of both s- and t, u-channel intermediate resonances.

The photon polarization in D (s) → K 1 (→ Kππ)γ decays can be extracted from an up-down asymmetry in the Kππ system, along the lines of the method known to B → K 1 (→ Kππ)γ decays. Charm physics is advantageous as partner decays exist: D + → K + 1 (→ Kππ)γ, which is standard model-like, and D s → K + 1 (→ Kππ)γ, which is sensitive to physics beyond the standard model in |∆c| = |∆u| = 1 transitions. The standard model predicts their photon polarizations to be equal up to U-spin breaking corrections, while new physics in the dipole operators can split them apart at order one level. We estimate the proportionality factor in the asymmetry multiplying the polarization parameter from axial vectors K 1 (1270) and K 1 (1400) to be sizable, up to the few O(10)% range. The actual value of the hadronic factor matters for the experimental sensitivity, but is not needed as an input to perform the null test. I. INTRODUCTIONCharm decay amplitudes are notoriously challenging due to an often overwhelming resonance contribution in addition to poor convergence of the heavy quark expansion. Yet, rare charm decays are of particular importance as they are sensitive to flavor and CP violation in the upsector, complementary to Kand B-physics. While the number of radiative and semileptonic |∆c| = |∆u| = 1 modes within reach of the flavor facilities BaBar, Belle, LHCb, BESIII, and Belle II is plenty, it needs dedicated efforts to get sufficient control over hadronic uncertainties to be able to test the standard model (SM). A useful strategy known as well to the presently much more advanced B-physics program is to custom-built observables "null tests", exploiting approximate symmetries of the SM, such as lepton universality, CP in b → s and c → u transitions, or SU (3) F . This allows to bypass a precise, first-principle computation of hadronic matrix elements which presently may not exist.In this work we provide a detailed study of the up-down asymmetry A UD in the angular * Electronic address: nico.adolph@tu-dortmund.de †

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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.