Vacuum-Polarization Corrections to the Hyperfine Structure of theμ+μ−Bound System

Abstract

The frequency shift $\Delta \nu$ due to vacuum polarization by electron pairs and hadrons is calculated for the hyperfine interval of the ${\mu }^{+}{\mu }^{-}$ bound system. These corrections contribute at the part-per-thousand level and lead to a total triplet-singlet splitting of $\nu +\Delta \nu =4.220\mathrm{}\times {10}^7$ MHz.