Radiative Corrections to the Muonium Hyperfine Structure. II. The $α(Zα)^2 $ Correction

Abstract

This is the second of a series of papers on the radiative corrections of order $α^2 (Zα)$, $α(Zα)^2$, and various logarithmic terms of order $α^4$, to the hyperfine structure of the muonium ground state. This paper deals with the $α(Zα)^2$ correction. Based on the NRQED bound state theory, we isolated the term of order $α(Zα)^2$ exactly. Our result $+16.904 2 (11) α(Zα)^2 E_F / π$ for the non-logarithmic part is consistent with the $α(Zα)^2$ part of Sapirstein's calculation and the recent result of Pachucki, and reduces the numerical uncertainty in the $α(Zα)^2$ term by two orders of magnitude.