Radiative corrections to the muonium hyperfine structure: The alpha(2)(Z alpha) 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 alpha(2)(Z alpha) radiative correction; Our result for the complete alpha(2)(Z alpha) 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 alpha(Z alpha)(2) term and logarithmic terms of order alpha(4). These terms will be treated in the subsequent papers.