Improved nuclear-structure corrections to the hyperfine splitting of electronic and muonic deuterium

TL;DR

This paper refines nuclear-structure corrections to hyperfine splitting in electronic and muonic deuterium using chiral effective field theory, reducing uncertainties and improving agreement with experiments.

Contribution

It introduces a new approach with chiral effective field theory for more accurate nuclear-structure corrections and uncertainty quantification in deuterium hyperfine splitting calculations.

Findings

Reduced uncertainty in two-photon exchange contributions.

Agreement with experimental data within 0.7 sigma for electronic deuterium.

Consistent results with previous pionless effective field theory calculations.

Abstract

We calculate the nuclear-structure correction to the hyperfine splitting in both electronic and muonic deuterium using interactions from chiral effective field theory. We explore the sensitivity to different parameterizations of the nucleon-nucleon force, study the convergence pattern in the order-by-order chiral expansion, and estimate remaining uncertainties. Our results are consistent with earlier calculations from pionless effective field theory, offering new insights for a robust uncertainty quantification. Thanks to the order-of-magnitude reduction in uncertainty achieved with chiral effective field theory, the two-photon exchange contribution in electronic deuterium agrees with experimental extractions within $0.7\sigma$, in contrast to the $2.7\sigma$ discrepancy observed in muonic deuterium. This study lays the groundwork for extending TPE calculations to HFS in heavier atomic systems.