Radiative Corrections to the Muonium Hyperfine Structure. II. The $α(Zα)^2 $ Correction

Details Radiative Corrections to the Muonium Hyperfine Structure. II. The $α(Zα)^2 $ Correction Radiative Corrections to the Muonium Hyperfine Structure. II. The $α(Zα)^2 $ Correction

1997-02-02

arxiv.org/abs/hep-ph/9702218v2

Phys. Rev. D, 55 (1997) 7267

Physics

High Energy Physics

High Energy Physics - Phenomenology

52 pages, RevTex and epsf.tex, 10 figures. Minor modifications

Scientific paper

10.1103/PhysRevD.55.7267

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 $+16.904 2 (11) \alpha(Z\alpha)^2 E_F / \pi$ 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.

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