Compatibility of the Updated $(g-2)_μ$, $(g-2)_e$ and PADME-Favored Couplings with the Preferred Region of ATOMKI X17

We re-evaluate the viability of a kinetically mixed dark photon ($A^{\prime}$) as a solution to the muon anomalous magnetic moment $(g-2)μ$ discrepancy and the ATOMKI nuclear anomalies near 17~MeV, using the final FNAL measurement and the latest theory predictions (BMW21, WP25). For $m_{A^{\prime}} = 17$~MeV, the allowed kinetic mixing parameter narrows to $\varepsilon_μ= 7.03(58)\times10^{-4}$ (WP25). We then directly compare the allowed region for the muon and X17 bands to those preferred by the electron magnetic moment measurements. For the electron, we obtain $\varepsilon_e = 1.19(15)\times10^{-3}$ (Cs, 2018) and $\varepsilon_e = 0.69(15)\times10^{-3}$ (Rb, 2020), based on two recent measurements of the fine structure constant compared to the most recent experimental value determined using a one-electron quantum cyclotron. This study focuses on the protophobic vector interpretation of X17 and assumes $\varepsilon_ν«\varepsilon_l$. While a mild tension persists, we identify a narrow overlapping region, $6.8\times10^{-4} \lesssim \varepsilon \lesssim 9.6\times10^{-4}$, between recent PADME results, the NA64 exclusion, and within the 2$σ$ preferred coupling region given by the Rb 2020 determination of $α_\varepsilon$. These results provide well-defined targets for future experimental searches and motivate further theoretical refinements, both of which will play a decisive role in assessing the validity of the ATOMKI anomaly claims. Of particular note is the fixed target X17 experiment to be conducted in Hall-B of Thomas Jefferson National Accelerator Facility in Summer of 2026.

💡 Research Summary

The paper presents a comprehensive re‑evaluation of a kinetically mixed dark photon (A′) with a mass around 17 MeV as a unified explanation for three seemingly unrelated anomalies: the muon anomalous magnetic moment (g‑2)μ, the electron anomalous magnetic moment (g‑2)e, and the excess of e⁺e⁻ pairs observed in several nuclear transitions by the ATOMKI collaboration (the so‑called X17 signal).

First, the authors update the muon (g‑2) discrepancy using the final Fermilab measurement (a_exp^μ = 116 592 071.5 (145) × 10⁻¹¹) together with three recent Standard Model predictions: the data‑driven HVP estimate from the 2020 g‑2 Theory Initiative (WP20), the BMW21 lattice‑QCD result, and the latest WP25 evaluation (2025). The discrepancies shrink dramatically: Δa_μ = 262 ± 45 × 10⁻¹¹ (WP20), 118 ± 69 × 10⁻¹¹ (BMW21), and 39 ± 64 × 10⁻¹¹ (WP25). Using the one‑loop dark‑photon contribution Δa_ℓ ≈ (α ε²/2π) F_V(m_A′/m_ℓ), the kinetic‑mixing parameter required to explain the muon anomaly at m_A′ = 17 MeV is ε_μ ≈ 7.03 (58) × 10⁻⁴ (WP25).

Second, the electron sector is treated with two independent high‑precision determinations of the fine‑structure constant α: the 2018 cesium recoil measurement (α⁻¹ = 137.035999046 (27)) and the 2020 rubidium recoil measurement (α⁻¹ = 137.035999206 (11)). Plugging these α values into the SM prediction for a_e yields opposite‑sign residuals: Δa_e = −102 (26) × 10⁻¹⁰ (Cs) and +34 (16) × 10⁻¹⁰ (Rb). Translating these residuals into kinetic‑mixing values gives ε_e ≈ 1.19 (15) × 10⁻³ (Cs) and ε_e ≈ 0.69 (15) × 10⁻³ (Rb). The two results are mildly tensioned but both lie within the 10⁻³ range required for the X17 interpretation.

Third, the ATOMKI observations are summarized. The collaboration reported >5σ excesses in internal pair creation for M1 transitions in ⁸Be, ⁴He, and ¹²C, consistent with a new vector boson of mass 16.7 ± 0.85 MeV. To evade the stringent π⁰ → γ A′ limit (ε ≲ 3 × 10⁻⁴ at 16.7 MeV), the boson must be “protophobic,” i.e., its coupling to protons is strongly suppressed relative to neutrons. Under this assumption, the preferred kinetic‑mixing range from the nuclear data is ε ≈ 2 × 10⁻⁴ – 1.3 × 10⁻³.

The paper then overlays the most recent laboratory constraints. NA64 at CERN excludes 1.2 × 10⁻⁴ < ε < 6.8 × 10⁻⁴ (90% CL) for a 16.7 MeV dark photon that decays visibly to e⁺e⁻. The PADME fixed‑target experiment, scanning √s = 16.4–17.4 MeV, observed a 1.8σ upward fluctuation near 16.9 MeV and set a 90% CL upper limit g_ve ≤ 5.6 × 10⁻⁴, which translates to ε ≲ 1.9 × 10⁻³. Combining NA64 and PADME leaves an allowed window 6.8 × 10⁻⁴ ≲ ε ≲ 9.6 × 10⁻⁴ that is not excluded by either experiment.

When the electron (g‑2) preferred values are taken into account, the Rb‑2020 result (ε_e ≈ 0.7 × 10⁻³) falls squarely inside this surviving window, while the Cs‑2018 value is slightly higher but still compatible within 2σ. Consequently, there exists a narrow overlapping region where the muon, electron, PADME, NA64, and ATOMKI preferred couplings all intersect. This region is extremely limited—essentially a thin “stripe” in the ε–m_A′ plane—but it demonstrates that a protophobic dark photon remains a viable simultaneous solution to all three anomalies.

The authors stress that the viability hinges on several assumptions: (i) the dark photon is purely vectorial with universal kinetic mixing (no axial component), (ii) neutrino couplings are negligible (ε_ν ≪ ε_e), and (iii) the branching ratio to invisible final states is essentially zero, so the NA64 visible‑decay limits apply directly. They also note that future improvements in the hadronic vacuum polarization (e.g., lattice QCD) and more precise α measurements could shift the (g‑2) bands and either enlarge or close the overlap.

Finally, the paper highlights the upcoming Hall‑B X17 experiment at Jefferson Lab (summer 2026), a fixed‑target search specifically designed to probe the 6.8–9.6 × 10⁻⁴ kinetic‑mixing window at 17 MeV. A positive signal would provide a decisive confirmation of the dark‑photon hypothesis, while a null result would effectively rule out the protophobic vector explanation for the ATOMKI anomaly. The authors conclude by urging coordinated efforts among PADME, NA64, upcoming muon‑electron (g‑2) experiments, and precision α determinations to fully map and test this narrow but phenomenologically rich parameter space.