Radiative-Recoil Corrections to HFS

Leading logarithmic recoil correction, relative order Za Lepage (1977) [8] Bodwin, Yennie (1978) [9] 2 ZaY HZay 11.179 

Nonlogarithmic recoil correction, relative order (Za) Bodwin, Yennie, Gregorio (1982) [12, 13] Wi (-81n2 + f ) -2.197 

Second order in mass ratio, relative order ZaY Blokland, Czarnecki, Melnikov (2002) [17] [fln f+ (f-. )lnf -h33C(3)-127r2ln2-l f + f] Y (Za) m rnl 0.065 

Logarithm squared correction, relative order ZotY Karshenboim (1993) [18] - ln2(Za)-i(l + a ) -0.043 

Mixed logarithm correction, relative order ZotY Kinoshita, Nio (1994) [19, 20] Karshenboim (1996) [21] -3 tln( a)-MnM -0.210 

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Radiative-Recoil Corrections to HFS 199 Table 10.1. Recoil Corrections... 

Nonlogarithmic radiative-recoil corrections to HFS were first calculated numerically in the Yennie gauge [35, 25] and then analytically in the Feynman gauge [31]... 

In the case of the polarization insertions the calculations may be simplified by simultaneous consideration of the insertions of both the electron and muon polarization loops [18, 19]. In such an approach one explicitly takes into account internal symmetry of the problem at hand with respect to both particles. So, let us preserve the factor 1/(1 - - m/M) in (9.9), even in calculation of the nonrecoil polarization operator contribution. Then we will obtain an extra factor m /m on the right hand side in (9.12). To facilitate further recoil calculations we could simply declare that the polarization operator contribution with this extra factor m /m is the result of the nonrecoil calculation but there exists a better choice. Insertion in the external photon lines of the polarization loop of a heavy particle with mass M generates correction to HFS suppressed by an extra recoil factor m/M in comparison with the electron loop contribution. Corrections induced by such heavy particles polarization loop insertions clearly should be discussed together with other radiative-recoil... 

Radiative-recoil corrections of order a Za)" m/M)Ep were never calculated completely. As we have mentioned in Subsect. 9.4.1.1 the leading logarithm squared contribution of order a Za) EF may easily be calculated if one takes as one of the perturbation potentials the potential corresponding to the electron electric form factor and as the other the potential responsible for the main Fermi contribution to HFS (see Fig. 10.16). Then one obtains the leading logarithm squared contribution in the form [18]... 

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