$A_{\textrm{CP}}[D_{(s)}^{0,+} \to V γ]$ from Large ${\cal O}_8$

CP-violation in $ΔA_{\textrm {CP}} = -0.154(29)$, in the $D^0 \to π^+π^-/K^+K^-$ system, is established and its central value is one order of magnitude above the naive Standard Model (SM) estimate. It remains unclear whether this is due to currently incalculable strong interaction matrix elements or genuine new physics (NP) such as a shift in ${\cal O}_8$ with a weak phase. We show that the interference of the long-distance (LD) terms with the ${\cal O}_8$ matrix element can give rise to $A_{\text{CP}}^{D \to V γ} = \textrm{few} \cdot 10^{-3}$ (for reference values ${\textrm{Im}}[C_8^{NP}] \approx 10^{-3}$). In addition, it is pointed out that the ratio of left- to right-handed (photon polarisation) LD amplitudes is measurable in time-dependent CP (TDCP) asymmetries. We argue that both theory and experimental consideration favour weak annihilation (WA) as the dominant LD contribution. More definite progress could be achieved by either computing the radiative corrections to WA or the measurement of the charged modes $D^+_{(d,s)} \to (ρ,K^{*})^+ γ$ and $D_s \to ρ^+ γ$.

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