An updated view on the ATOMKI nuclear anomalies

Abstract: In view of the latest experimental results recently released by the ATOMKI collaboration, we critically re-examine the possible theoretical interpretation of the observed anomalies in terms of a new BSM boson $X$ with mass $\sim17\;$MeV. To this end we employ a multipole expansion method and give an estimate for the range of values of the nucleon couplings to the new light state in order to match the experimental observations. Our conclusions identify the axial vector state as the most promising candidate, while other spin/parity assignments seems disfavored for a combined explanation. This results is however based on an order of magnitude estimate for the, currently unknown, axial nuclear matrix element of the $^{12}$C transition, that needs then to be evaluated before being able to draw a definite conclusion. Intriguingly, an axial vector state can also simultaneously accommodate other experimental anomalies, {\emph{i.e.}} the KTeV anomaly in $\pi^0 \to e^+ e^-$ decay while being compatible with the conflicting measurements of the anomalous magnetic moment of the electron $(g-2)_e$ and other constraints on the electron couplings of the $X$ boson. The PADME experiment will completely cover the relevant region of the parameter space, thus allowing for a strong test of the existence of the $X$ particle.