Radiative corrections to the muonium hyperfine structure .2. The alpha(Z alpha)(2) correction

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 ground state. This paper deals with the alpha(Z alpha)(2) correction. Based on the NRQED bound state theory, we isolated the term of order alpha(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 by 2 orders of magnitude.