Hyperfine structure of excited state of muonic helium atom

TL;DR

This paper calculates the hyperfine splitting of an excited muonic helium atom state, incorporating higher-order corrections for improved accuracy, and provides a precise value for the splitting frequency.

Contribution

The study introduces refined calculations of hyperfine splitting in muonic helium, including new recoil, vacuum polarization, and electron vertex corrections up to second order in alpha.

Findings

Hyperfine splitting value of 4295.66 MHz obtained.

Enhanced accuracy over previous calculations.

Inclusion of higher-order quantum corrections.

Abstract

The recoil, vacuum polarization and electron vertex corrections of first and second orders in the fine structure constant $\alpha$ and the ratio of electron to muon and electron to \alpha-particle masses are calculated in the hyperfine splitting of the $1s^{(e)}_{1/2}2s^{(\mu)}_{1/2}$ state of muonic helium atom (\mu e ^4_2He) on the basis of a perturbation theory. We obtain total result for the muonically excited state hyperfine splitting $\Delta \nu^{hfs}=4295.66$ MHz which improves previous calculations due to the account of new corrections and more accurate treatment of the electron vertex contribution.