Radiative corrections to the muonium hyperfine structure: Theα2(Zα) correction

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 ${\mathrm{\alpha }}^2$(Zα) radiative correction. Our result for the complete ${\mathrm{\alpha }}^2$(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 ${\mathrm{\alpha }}^4$. These terms will be treated in the subsequent papers. © 1996 The American Physical Society.