Compatibility of the Updated $(g-2{)}_{\mu }$, $(g-2{)}_e$ and PADME-Favored Couplings with the Preferred Region of ATOMKI X17

Abstract

We re-evaluate the viability of a kinetically mixed dark photon ($A^{\prime }$) as a solution to the muon anomalous magnetic moment $(g-2)\mu$ 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 ${\epsilon }_{\mu }=7.03(58)\times 10^{-4}$ (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 ${\epsilon }_e=1.19(15)\times 10^{-3}$ (Cs, 2018) and ${\epsilon }_e=0.69(15)\times 10^{-3}$ (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 ${\epsilon }_{\nu }<<{\epsilon }_l$. While a mild tension persists, we identify a narrow overlapping region, $6.8\times 10^{-4}\lesssim \epsilon \lesssim 9.6\times 10^{-4}$, between recent PADME results, the NA64 exclusion, and within the 2$\sigma$ preferred coupling region given by the Rb 2020 determination of ${\alpha }_{\epsilon }$. 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.

Comments: 15 Pages, 2 figures