Precision Positronium Spectroscopy as a Test of the Helium Ionization Energy Anomaly

Precise measurements of the metastable helium (1s)(2s)$\,^3S_1$ ionization energy have revealed a 9$\sigma$ discrepancy with QED theory that persists in isotopic measurements, suggesting a leptophilic bosonic interaction as a possible explanation. A subsequent investigation of such interactions has concluded that only a scalar boson interaction is consistent with the He observations. Taking this as a starting point, we derive the response of positronium energy levels to the corresponding finite-range Yukawa potential, using exact hydrogenic matrix elements and a numerical helium calculation. Across the viable mediator-mass range of 0-800 eV, the He anomaly interpreted in this way implies a positronium 1$^3$S$_1 \rightarrow 2^3$S$_1$ shift ranging from 0.250-0.850 MHz, and a 2S-ionization shift of 0.14-0.21 MHz. We discuss the feasibility of observing these shifts experimentally.