What Does Precision Spectroscopy Actually Constrain about X17 Couplings?

Abstract

Can precision spectroscopy disentangle the individual couplings of the X17 boson? Within a leading one-body model, we combine electronic and muonic spectroscopy of hydrogen, deuterium and helium with lepton magnetic moments. We show that hydrogen-deuterium comparisons can lose neutron sensitivity through cancellations, while the combined observables restore generic local identifiability without guaranteeing finite individual bounds. The unrestricted fit admits formally unbounded nucleon-coupling directions, some of which violate the assumptions underlying the physical model. Finite-coupling tests nevertheless reveal statistically compatible solutions, with bounds dependent on nuclear responses and physical assumptions. Our results establish what precision measurements genuinely constrain and what additional information is required to extract meaningful limits on X17 couplings.