Testing Quantum Electrodynamics with Positronium State

Penin, Alexander A.

doi:10.22323/1.211.0074

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2015

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“…New measurement of the positronium HFS splitting is now planned at J-PARC [17]. All theoretical contributions to HFS in positronium of order mα 6 and logarithmic corrections of order mα 7 are already known, see, e.g., reviews in [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Hard three-loop corrections to hyperfine splitting in positronium and muonium

Eides

Shelyuto

2015

Phys. Rev. D

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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 mα 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 mα 7 to hyperfine splitting in positronium.

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