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

Abstract

This is the first of a series of papers on a systematic application of the NRQED bound state theory of Caswell and Lepage to higher-order radiative corrections to the hyperfine structure of the muonium ground state. This paper describes the calculation of the $α^2 (Zα)$ radiative correction. Our result for the complete $α^2 (Zα)$ correction is 0.424(4) kHz, which reduces the theoretical uncertainty significantly. The remaining uncertainty is dominated by that of the numerical evaluation of the nonlogarithmic part of the $α(Zα)^2$ term and logarithmic terms of order $α^4$.