Radiative-nonrecoil corrections of orderα2(Zα)5to the Lamb shift

Abstract

We present results for the corrections of order α 2 (Zα) 5 to the Lamb shift. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We confirm results obtained by other groups and improve their precision. Values of the 32 "master integrals" for this and similar problems are provided.

Two-loop corrections to the Lamb shift

“…Results for individual diagrams can be found in Ref. [15]. The best results for the two subsets prior to our calculation have been published in Ref.…”

Radiative-nonrecoil corrections of orderα2(Zα)EFto the hyperfine splitting of muonium

“…(27) The sum of all central values in the second column of Tables I and II gives the coefficient 0.77099 in Eq. (19). The error of that result, however, is not obtained from the sum of the errors of the diagrams in the tables.…”

“…We used the so-called Laporta algorithm [16,17] as implemented in the MATHEMATICA package FIRE [18], to reduce the problem to 32 master integrals. The master integrals for this calculation are the same ones we found in [19]; all definitions and results for the integrals can be found in this reference. However, one change was made for this calculation.…”

“…(19) applies to any hydrogen-like atom]. In order to compute these corrections, we consider the scattering amplitude…”

Virtual Delbrück scattering and the Lamb shift in light hydrogenlike atoms

“…PNRQED contains potential electron modes and ultra-soft photons. The light-by-light contribution to the hydrogen spectrum was previously considered in [18,[40][41][42][43]. In that case, all the loop momenta are hard (k ∼ m e ) and the diagram shown in Fig.…”