Hyperfine structure of S-states in muonic deuterium

TL;DR

This paper calculates high-order quantum electrodynamics corrections to the hyperfine structure of muonic deuterium's S-states, providing precise theoretical values for upcoming experimental comparisons.

Contribution

It offers the first comprehensive calculation of order α^5 and α^6 corrections to hyperfine splitting in muonic deuterium, including relativistic, vacuum polarization, nuclear structure, and recoil effects.

Findings

Hyperfine splitting for 1S state: 50.2814 meV

Hyperfine splitting for 2S state: 6.2804 meV

Hyperfine interval Δ12: -0.0379 meV

Abstract

On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $\alpha^5$ and $\alpha^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{hfs}(1S)=50.2814$ meV (1S state) and $\Delta E^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. The hyperfine structure interval $\Delta_{12}=8\Delta E^{hfs}(2S)-\Delta E^{hfs}(1S)=-0.0379$ meV can be used for precision check of quantum electrodynamics predictions for muonic deterium.