Light-by-Light Scattering Nonlogarithmic Corrections to Hyperfine Splitting in Muonium

We consider three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These diagrams produce both recoil and nonrecoil contributions to hyperfine splitting. Recoil corrections are enhanced by large logarithms of the muon-electron mass ratio. Both nonrecoil and logarithmically enhanced radiative-recoil corrections where calculated some time ago. Here we calculate nonlogarithmic radiative-recoil corrections generated by the insertions of the light-by-light scattering block.Comment: Minor corrections, version to be published in Phys. Rev.

Hard Three-Loop Corrections to Hyperfine Splitting in Positronium and Muonium

We consider hard three-loop corrections to hyperfine splitting in muonium and positronium generated by the diagrams with closed electron loops. There are six gauge-invariant sets of such diagrams that generate corrections of order $m\alpha^7$. The contributions of these diagrams are calculated for an arbitrary electron-muon mass ratio without expansion in the small mass ratio. We obtain the formulae for contributions to hyperfine splitting that in the case of small mass ratio describe corrections for muonium and in the case of equal masses describe corrections for positronium. First few terms of the expansion of hard corrections in the small mass ratio were earlier calculated for muonium analytically. We check numerically that the new results coincide with the sum of the known terms of the expansion in the case of small mass ratio. In the case of equal masses we obtain hard nonlogarithmic corrections of order $m\alpha^7$ to hyperfine splitting in positronium.Comment: 19 pages, 8 figure

One-Loop Electron Vertex in Yennie Gauge

We derive a compact Yennie gauge representation for the off-shell one-loop electron-photon vertex, and discuss it properties. This expression is explicitly infrared finite, and it has proved to be extremely useful in multiloop calculations in the QED bound state problem.Comment: Revtex, 12 pp., 1 fig., one reference added. Two misprints in intermediate formulae correcte

Two-Loop Electron Factor Contribution to Lamb Shift in Muonium and Positronium

We calculate hard spin-independent contributions to energy levels in muonium and positronium which are due to radiatively corrected electron factor insertion in two-photon exchange diagrams. Calculation of these corrections is motivated by the new round of precise measurements of spin-independent transition frequencies in muonium and positronium.Comment: 7 pages, 3 figure

One More Hard Three-Loop Correction to Parapositronium Energy Levels

A hard three-loop correction to parapositronium energy levels of order mα7 is calculated. This nonlogarithmic contribution is due to the insertions of one-loop photon propagator in the fermion lines in the diagrams with virtual two-photon annihilation. We obtained ΔE = 0.03297(2)(mα7 / π3) for this energy shift

Three-Loop Contributions to Hyperfine Splitting: Muon Loop Light-By-Light Insertion and Other Closed Lepton Loops

The muon and tauon light-by-light scattering contributions to hyperfine splitting in muonium are calculated. These results conclude the calculation of all hard three-loop contributions to hyperfine splitting generated by the graphs with closed fermion loops. We discuss the special role that the lepton anomalous magnetic moments play in these calculations. The full result for all three-loop radiative-recoil corrections to hyperfine splitting generated by the graphs with closed lepton loops is presented