A kinetically mixed dark photon produced in $D^0\to \gamma A^{\prime }$ probes the timelike electromagnetic current at $q^2=m_{A^{\prime }}^2$, where resolved vector-meson structure can render a pointlike continuation from the real photon point inadequate. The magnitudes of the ${\rho }^0$ and $\varphi$ pole residues are normalized to measured radiative charm data and electronic vector-meson widths, while the $\omega$ contribution is bounded using the experimental upper limit on $D^0\to \gamma \omega$. Treating the parity conserving and parity violating amplitudes as a complex vector with two components, norm inequalities yield a lower envelope valid for arbitrary relative phases and orientations in this amplitude space once an upper bound on the smooth remainder is specified. At the $\varphi$ pole, the combined ceiling of the explicit non-$\varphi$ poles amounts to only 1.93% of the $\varphi$ pole amplitude norm for the central inputs. Consequently, complete cancellation at resonance requires the smooth remainder to reach at least 98.1% of the peak $\varphi$ pole amplitude norm within the adopted pole decomposition. For the representative $B_3$ benchmark, which bounds the norm of the smooth remainder by half the peak $\varphi$ pole amplitude, the conditional floor of the reduced branching fraction at resonance is ${\widehat{\mathcal{B}}}_{\mathrm{low}}^{(B_3)}(m_{\varphi }^2)=(1.89_{-0.14}^{+0.13})\times {10}^{-4}$. The corresponding lower envelope remains positive within approximately $\pm 3.5\mathrm{MeV}$ of the $\varphi$ pole. At resonance, this $B_3$ benchmark floor exceeds the pointlike comparison baseline, normalized to the experimental upper limit on $D^0\to \gamma \gamma$, by a factor of $(3.23\pm 0.23)\times {10}^2$. These results demonstrate that resolved hadronic structure can substantially affect dark photon production near the $\varphi$ resonance.

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• Leptonic, semileptonic & radiative decays
• Rare decays
• Charmed mesons
• Hypothetical gauge bosons
• Vector mesons