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 ra diative corrections to the hyperfine structure of the muonium ground s tate. This paper describes the calculation of the alpha(2)(Z alpha) ra diative correction; Our result for the complete alpha(2)(Z alpha) corr ection is 0.424(4) kHz, which reduces the theoretical uncertainty sign ificantly. The remaining uncertainty is dominated by that of the numer ical evaluation of the nonlogarithmic part of the alpha(Z alpha)(2) te rm and logarithmic terms of order alpha(4). These terms will be treate d in the subsequent papers.