Analytic calculation of radiative-recoil corrections to muonium hyperfine splitting: Electron-line contribution

Eides, Michael I.; Karshenboim, Savely G.; Shelyuto, Valery A.

doi:10.1016/0003-4916(91)90016-2

Cited by 52 publications

(49 citation statements)

References 22 publications

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“…1. It is well known that insertion of radiative corrections suppresses the low integration momentum region, see, e.g., [5,6,23]. Hence, all diagrams in …”

Section: Fig 1 Diagrams With Two-photon Exchangesmentioning

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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“…1. It is well known that insertion of radiative corrections suppresses the low integration momentum region, see, e.g., [5,6,23]. Hence, all diagrams in …”

Section: Fig 1 Diagrams With Two-photon Exchangesmentioning

confidence: 99%

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

Eides

Shelyuto

2015

Phys. Rev. D

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“…In the region of small momenta one uses the condition µk ≪ 1 to simplify the integrand, and in the region of large momenta the same goal is achieved with the help of the condition k ≫ 1. Note that for k ≃ σ both conditions on the integration momenta are valid simultaneously, so in the sum of the low-momenta and high-momenta integrals all σ-dependent terms cancel and one obtains a σ-independent result for the total momentum integral (for a more detailed discussion of this method, see, e.g., [11]). All contributions, up to and including the corrections quadratic in the small mass ratio m/M, were analytically calculated earlier in this framework [6,10] (see also [11,5]).…”

Section: Radiative-recoil Correction Of Order α(Zα)(m/m ) E Fmentioning

confidence: 99%

Three-loop radiative-recoil corrections to hyperfine splitting in muonium

Eides¹,

Grotch²,

Shelyuto³

2005

Can. J. Phys.

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We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.

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“…Integration over t is facilitated by the simple observation that the t-integral may be written as an integral over a 2 t with the upper limit a 2 . After this transformation all dependence of the new integral on x is hidden in this upper integration limit, and we can get rid of the third Feynman parameter integrating by parts over x (for more details see [7]) The contribution to the Lamb shift generated by the spanning photon insertion in the electron line in Fig. 1 is calculated with the help of an explicit expression for the jellyfish diagram.…”

Section: Vertex Contributionmentioning

confidence: 99%

Radiative-recoil corrections of orderα(Zα)5(m/M)mto the Lamb shift revisited

2001

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The results and main steps of an analytic calculation of radiative-recoil corrections of order α(Zα) 5 (m/M )m to the Lamb shift in hydrogen are presented. The calculations are performed in the infrared safe Yennie gauge. The discrepancy between two previous numerical calculations of these corrections existing in the literature is resolved. Our new result eliminates the largest source of the theoretical uncertainty in the magnitude of the deuterium-hydrogen isotope shift.

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Analytic calculation of radiative-recoil corrections to muonium hyperfine splitting: Electron-line contribution

Cited by 52 publications

References 22 publications

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

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

Three-loop radiative-recoil corrections to hyperfine splitting in muonium

Radiative-recoil corrections of orderα(Zα)5(m/M)mto the Lamb shift revisited

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