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Recent anomalies in $^8$Be and $^4$He nuclear decays can be explained bypostulating a fifth force mediated by a new boson $X$. The distributions ofboth transitions are consistent with the same $X$ mass, 17 MeV, providingkinematic evidence for a single new particle explanation. In this work, weexamine whether the new results also provide dynamical evidence for a newparticle explanation, that is, whether the observed decay rates of bothanomalies can be described by a single hypothesis for the $X$ boson'sinteractions. We consider the observed $^8$Be and $^4$He excited nuclei, aswell as a $^{12}$C excited nucleus; together these span the possible $J^P$quantum numbers up to spin 1. For each transition, we determine whether scalar,pseudoscalar, vector, or axial vector $X$ particles can mediate the decay, andwe construct the leading operators in a nuclear physics effective field theorythat describes them. Assuming parity conservation, the scalar case is excludedand the pseudoscalar case is highly disfavored. Remarkably, however, theprotophobic vector gauge boson, first proposed to explain only the $^8$Beanomaly, also explains the $^4$He anomaly within experimental uncertainties. Wepredict signal rates for other closely related nuclear measurements, which, ifconfirmed, will provide overwhelming evidence that a fifth force has beendiscovered.

Dynamical Evidence For a Fifth Force Explanation of the ATOMKI Nuclear Anomalies