Radiative Corrections to the Muonium Hyperfine Structure. II. The $\alpha (Z\alpha {)}^2$ Correction

Abstract

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 $+16.9042(11)\alpha (Z\alpha {)}^2{E}_F/\pi$ 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 two orders of magnitude.

arXiv comment52 pages, RevTex and epsf.tex, 10 figures. Minor modifications

References in corpus (4)

• Improved Nonrelativistic QCD for Heavy Quark Physics
• Radiative Corrections to the Muonium Hyperfine Structure. I. The ${\alpha }^2(Z\alpha )$ Correction
• Improved Theory of the Muonium Hyperfine Structure
• Order m alpha^8 Contributions to the Decay Rate of Orthopositronium

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