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

Abstract

This is the second of a series of papers on the radiative corrections of order $\hat{I}{\pm }^2(Z\hat{I}\pm )$, $\hat{I}\pm (Z\hat{I}\pm {)}^2$, and various logarithmic terms of order $\hat{I}{\pm }^4$, to the hyperfine structure of the muonium ground state. This paper deals with the $\hat{I}\pm (Z\hat{I}\pm {)}^2$ correction. Based on the NRQED bound state theory, we isolated the term of order $\hat{I}\pm (Z\hat{I}\pm {)}^2$ exactly. Our result $+16.9042(11)\hat{I}\pm (Z\hat{I}\pm {)}^2{E}_F/\ddot{I}€$ for the non-logarithmic part is consistent with the $\hat{I}\pm (Z\hat{I}\pm {)}^2$ part of Sapirstein's calculation and the recent result of Pachucki, and reduces the numerical uncertainty in the $\hat{I}\pm (Z\hat{I}\pm {)}^2$ term by two orders of magnitude.

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