M. Nio et T. Kinoshita, RADIATIVE-CORRECTIONS TO THE MUONIUM HYPERFINE-STRUCTURE .2. THE ALPHA(Z-ALPHA)(2) CORRECTION, Physical review. D. Particles and fields, 55(11), 1997, pp. 7267-7290
This is the second of a series of papers on the radiative corrections
of order alpha(2)(Z alpha), alpha(Z alpha)(2), and various logarithmic
terms of order alpha(4), to the hyperfine structure of the muonium gr
ound state. This paper deals with the alpha(Z alpha)(2) correction. Ba
sed on the NRQED bound state theory, we isolated the term of order alp
ha(Z alpha)(2) exactly. Our result +16.904 2 (11)alpha(Z alpha)E-2(F)/
pi for the non-logarithmic part is consistent with the alpha(Z alpha)(
2) part of Sapirstein's calculation and the recent result of Pachucki,
and reduces the numerical uncertainty in the alpha(Z alpha)(2) term b
y 2 orders of magnitude.