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Updated $(g-2)_μ$, $(g-2)_e$ and PADME-Favored Couplings Narrowly Compatible with the Preferred Region of ATOMKI X17, Given a Protophobic Vector Interpretation

Emrys Peets

Abstract

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. While a mild tension persists, we identify a narrow overlapping region, $3.4\times10^{-4} \lesssim \varepsilon \lesssim 5.6\times10^{-4}$, between recent PADME results and NA64 exclusions, compatible with a protophobic gauge boson interpretation. 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.

Updated $(g-2)_μ$, $(g-2)_e$ and PADME-Favored Couplings Narrowly Compatible with the Preferred Region of ATOMKI X17, Given a Protophobic Vector Interpretation

Abstract

We re-evaluate the viability of a kinetically mixed dark photon () as a solution to the muon anomalous magnetic moment discrepancy and the ATOMKI nuclear anomalies near 17~MeV, using the final FNAL measurement and the latest theory predictions (BMW21, WP25). For ~MeV, the allowed kinetic mixing parameter narrows to (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 (Cs, 2018) and (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. While a mild tension persists, we identify a narrow overlapping region, , between recent PADME results and NA64 exclusions, compatible with a protophobic gauge boson interpretation. 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.
Paper Structure (15 sections, 37 equations, 3 figures, 1 table)

This paper contains 15 sections, 37 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Current Values of the $\Delta a_\mu$ and $\Delta a_e$
  3. Latest Experimental Measurement and Standard Model Predictions for $a_\mu$
  4. Anomalous Magnetic Moment of the Electron
  5. Heavy Photon mixing with a lepton at Vacuum level
  6. Calculating Leptonic Kinetic Mixing Parameters
  7. Current Feasibility of a 17 MeV Vector Boson
  8. ATOMKI Measurements
  9. Additional Experimental Constraints at 17 MeV
  10. Results
  11. Determining $\varepsilon_\mu$ using $\Delta a_\mu$
  12. Determining $\varepsilon_e$ using $\Delta a_e$
  13. Conclusion
  14. Impact of the 2025 $(g-2)_\mu$ determination.
  15. Acknowledgements

Figures (3)

  • Figure 1: Leading-order heavy photon contribution to the gyromagnetic ratio of a lepton.
  • Figure 2: Comparison of $(g-2)_\mu$ allowed parameter space using (top to bottom): WP20, BMW21, and WP25 theory predictions.
  • Figure 3: Overlay of ATOMMKI preferred $\varepsilon_e$ (yellow box) and allowable $1\sigma$, $2\sigma$ contours on $\varepsilon_e$, $\varepsilon_\mu$ from fine structure precision measurements on the $^{87}$Rb, $^{133}$Cs and the FNAL final average $a_\mu$ respectively. The black lines indicate the current limits set by (top) PADME, and (bottom) NA64. In between these lines is the parameter space still viable for the protophobic interpretation of X17.