Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections

Measurements of the difference between the squared charge radii of the helion ($^3$He nucleus) and the $\alpha$-particle ($^4$He nucleus) have been characterized by longstanding tensions, recently spotlighted in the 3.6 $\sigma$ discrepancy of the extractions from ordinary atoms versus those from muonic atoms. Here, we present a novel analysis of uncertainties in nuclear structure corrections that must be supplied by theory to enable the extraction of the difference in radii from spectroscopic experiments. We use modern Bayesian inference techniques to quantify uncertainties stemming from the truncation of the chiral effective field theory expansion of the nuclear force for both muonic and ordinary atoms. With the new nuclear structure input, the helium isotope-shift puzzle cannot be explained, rather it is reinforced to a 4 $\sigma$ discrepancy.