Reduced Theoretical Error for QED Tests with 4He+ Spectroscopy

TL;DR

This paper uses effective field theory to identify spectroscopic measurement combinations in 4He+ ions that significantly reduce theoretical uncertainties, enabling more precise tests of quantum electrodynamics independent of nuclear uncertainties.

Contribution

It introduces a method to construct spectroscopic measurement combinations in 4He+ that minimize theoretical errors, surpassing previous limitations from nuclear matrix element uncertainties.

Findings

Reduced theoretical error in selected measurement combinations

Independence from short-range physics effects up to a certain order

Enhanced precision in QED tests using 4He+ spectroscopy

Abstract

We apply point-particle effective field theory (PPEFT) to electronic and muonic 4He+ ions, and use it to identify linear combinations of spectroscopic measurements for which the theoretical uncertainties are much smaller than for any particular energy levels. The error is reduced because these combinations are independent of all short-range physics effects up to a given order in the expansion in the small parameters R/a_B and(Z alpha) (where R and a_B are the ion's nuclear and Bohr radii). In particular, the theory error is not limited by the precision with which nuclear matrix elements can be computed, or compromised by the existence of any novel short-range interactions, should these exist. These combinations of 4He+ measurements therefore provide particularly precise tests of QED. The restriction to 4He+ arises because our analysis assumes a spherically symmetric nucleus, but the argument used is more general and extendable to both nuclei with spin, and to higher orders in R/a_B and (Z alpha).