Ground State Hyperfine Structure of Muonic Helium Atom

TL;DR

This paper provides a refined calculation of the hyperfine splitting in muonic helium, incorporating new quantum corrections, resulting in a more accurate theoretical value that aligns closely with experimental data.

Contribution

It introduces updated calculations of vacuum polarization, electron vertex, and nuclear structure corrections for muonic helium's hyperfine splitting, improving previous theoretical estimates.

Findings

Calculated hyperfine splitting as 4465.526 MHz

Remaining discrepancy with experiment is 0.522 MHz

Theoretical error range includes higher order corrections

Abstract

On the basis of the perturbation theory in the fine structure constant $\alpha$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(\mu e ^4_2He)$. We obtain total result for the ground state hyperfine splitting $\Delta \nu^{hfs}=4465.526$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections. The remaining difference between the theoretical result and experimental value of the hyperfine splitting equal to 0.522 MHz lies in the range of theoretical error and requires the subsequent investigation of higher order corrections.