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

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

doi:10.1016/0003-4916(91)90017-3

Cited by 20 publications

(46 citation statements)

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“…Complete formal analysis of the recoil corrections in the framework of the relativistic two-particle equations, with derivation of all relevant kernels, perturbation theory contributions, and necessary subtraction terms may be performed along the same lines as was done for hyperfine splitting in [129]. However, these results may also be understood without a cumbersome formalism by starting with the simple scattering approximation.…”

Section: Fig 35 Irreducible Kernels With Arbitrary Number Of the Exmentioning

confidence: 99%

“…More interesting is the low momentum behavior of the electron factor. Due to the generalized low energy theorem for the Compton scattering (see, e.g., [129]), the electron factor has a pole at small momenta and the residue at this pole is completely determined by the one loop anomalous magnetic moment. Hence, naive substitution of the electron factor in eq.…”

Section: Fig 68 Diagrams With Radiative Insertions In the Electron mentioning

confidence: 99%

“…The crucial observation, which greatly facilitates the calculations, is that the scattering approximation (skeleton integral approach) is adequate for calculation of these corrections (see, e.g., a detailed proof in [129]). As in the case of the radiative corrections to the Lamb shift discussed in Section IX A, radiative corrections to HFS of order α(Zα)E F are given by the matrix elements of the diagrams with all external electron lines on the mass shell calculated between free electron spinors.…”

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confidence: 99%

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Theory of light hydrogenlike atoms

2001

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The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion He + , and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium. *

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Section: Fig 35 Irreducible Kernels With Arbitrary Number Of the Exmentioning

confidence: 99%

Section: Fig 68 Diagrams With Radiative Insertions In the Electron mentioning

confidence: 99%

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Theory of light hydrogenlike atoms

2001

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“…5, 6 we include in the integral radiatively corrected virtual Compton scattering amplitude instead of the skeleton one. A generalized low energy theorem holds for the virtual Compton scattering amplitude with subtracted anomalous magnetic moment contribution (see more on this subtraction below) [7,8]. According to this theorem the electron (muon) factor L µν (k) is suppressed by an additional factor k 2 /m 2 (k 2 /M 2 ) in comparison with the respective skeleton factor.…”

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confidence: 99%

“…5 with the electron polarization loops generate nonrecoil and logarithm squared, single-logarithmic, and nonlogarithmic radiative-recoil contributions to HFS. It turns out that the gauge invariant anomalous magnetic moment in these diagrams does not generate radiative-recoil corrections (see, e.g., [8,9]). Then the radiatively corrected electron factor L µν provides an additional suppression factor k 2 /m 2 in the skeleton integral over the exchanged momenta.…”

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Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium: Diagrams with Polarization Loops

Eides

Shelyuto

2009

Phys. Rev. Lett.

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We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order α 3 (m/M )E F generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining these corrections with the older results we obtain total contribution to hyperfine splitting generated by all diagrams with electron and muon polarization loops. Calculation of this contribution completes an important stage in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. The new results 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.Typeset by REVT E X 1 arXiv:0907.1923v2 [hep-ph]

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