Dynamical evidence for a fifth force explanation of the ATOMKI nuclear anomalies

Recent anomalies in Be-8 and He-4 nuclear decays can be explained by postulating a fifth force mediated by a new boson X. The distributions of both transitions are consistent with the same X mass, 17 MeV, providing kinematic evidence for a single new particle explanation. In this work, we examine whether the new results also provide dynamical evidence for a new particle explanation, that is, whether the observed decay rates of both anomalies can be described by a single hypothesis for the X boson's interactions. We consider the observed Be-8 and He-4 excited nuclei, as well as a C-12 excited nucleus; together these span the possible J(P) quantum numbers up to spin 1 for excited nuclei. For each transition, we determine whether scalar, pseudoscalar, vector, or axial vector X particles can mediate the decay, and we construct the leading operators in a nuclear physics effective field theory that describes them. Assuming parity conservation, the scalar case is excluded and the pseudoscalar case is highly disfavored. Remarkably, however, the protophobic vector gauge boson, first proposed to explain only the Be-8 anomaly, also explains the He-4 anomaly within experimental uncertainties. We predict signal rates for other closely related nuclear measurements, which, if confirmed by the ATOMKI group and others, would provide overwhelming evidence that a fifth force has been discovered.