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Tenth-Order QED Lepton Anomalous Magnetic Moment --- Eighth-Order Vertices Containing a Second-Order Vacuum Polarization
High Energy Physics - Phenomenology · Submitted 13 Oct 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The sum of all these contributions to the electron g-2 is $-7.7407(49) (\alpha/\pi)^5$.
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The abstract, sentence by sentence
This paper reports the evaluation of the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set of 2072 Feynman diagrams, called Set IV, which are obtained by inserting a second-order lepton vacuum-polarization loop into 518 eighth-order vertex diagrams of four-photon exchange type. The numerical evaluation is carried out by the adaptive-iterative Monte-Carlo integration routine vegas using the fortran codes written by the automatic code-generating algorithm gencodeN. Some of the numerical results are confirmed by comparison with the values of corresponding integrals that have been obtained previously by a different method. The result for the mass-independent contribution of the Set IV to the electron g-2 is $-7.7296 (48) (\alpha/\pi)^5$. There is also a small mass-dependent contribution to the electron g-2 due to the muon loop: $-0.01136 (7) (\alpha/\pi)^5$. The contribution of the tau-lepton loop is $-0.0000937(104)(\alpha/\pi)^5$. The sum of all these contributions to the electron g-2 is $-7.7407(49) (\alpha/\pi)^5$. The same set of diagrams enables us to evaluate the contributions to the muon g-2 from the electron loop, muon loop, and tau-lepton loop. They add up to $-46.95 (17) (\alpha/\pi)^5$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper reports the evaluation of the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set of 2072 Feynman diagrams, called Set IV, which are obtained by inserting a second-order lepton vacuum-polarization loop into 518 eighth-order vertex diagrams of four-photon exchange type. | contribution 1.00 | 0.94 | 0.16 | asserted 1.00 |
| s1 | The numerical evaluation is carried out by the adaptive-iterative Monte-Carlo integration routine vegas using the fortran codes written by the automatic code-generating algorithm gencodeN. | method 1.00 | 0.91 | 0.02 | asserted 1.00 |
| s2 | Some of the numerical results are confirmed by comparison with the values of corresponding integrals that have been obtained previously by a different method. | method 0.96 | 0.72 | 0.02 | asserted 0.93 |
| s3 | The result for the mass-independent contribution of the Set IV to the electron g-2 is $-7.7296 (48) (\alpha/\pi)^5$. | result 1.00 | 0.96 | 0.48 | asserted 1.00 |
| s4 | There is also a small mass-dependent contribution to the electron g-2 due to the muon loop: $-0.01136 (7) (\alpha/\pi)^5$. | result 1.00 | 0.93 | 0.05 | asserted 1.00 |
| s5 | The contribution of the tau-lepton loop is $-0.0000937(104)(\alpha/\pi)^5$. | result 1.00 | 0.93 | 0.03 | asserted 1.00 |
| s6 | The sum of all these contributions to the electron g-2 is $-7.7407(49) (\alpha/\pi)^5$. | result 1.00 | 0.95 | 0.43 | asserted 1.00 |
| s7 | The same set of diagrams enables us to evaluate the contributions to the muon g-2 from the electron loop, muon loop, and tau-lepton loop. | contribution 0.89 | 0.92 | 0.04 | asserted 0.97 |
| s8 | They add up to $-46.95 (17) (\alpha/\pi)^5$. | result 1.00 | 0.95 | 0.15 | asserted 1.00 |
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Original abstract
This paper reports the evaluation of the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set of 2072 Feynman diagrams, called Set IV, which are obtained by inserting a second-order lepton vacuum-polarization loop into 518 eighth-order vertex diagrams of four-photon exchange type. The numerical evaluation is carried out by the adaptive-iterative Monte-Carlo integration routine vegas using the fortran codes written by the automatic code-generating algorithm gencodeN. Some of the numerical results are confirmed by comparison with the values of corresponding integrals that have been obtained previously by a different method. The result for the mass-independent contribution of the Set IV to the electron g-2 is $-7.7296 (48) (\alpha/\pi)^5$. There is also a small mass-dependent contribution to the electron g-2 due to the muon loop: $-0.01136 (7) (\alpha/\pi)^5$. The contribution of the tau-lepton loop is $-0.0000937(104)(\alpha/\pi)^5$. The sum of all these contributions to the electron g-2 is $-7.7407(49) (\alpha/\pi)^5$. The same set of diagrams enables us to evaluate the contributions to the muon g-2 from the electron loop, muon loop, and tau-lepton loop. They add up to $-46.95 (17) (\alpha/\pi)^5$.
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5 arXiv papers cite this in 7 sentences
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By gencodeN and its modifications for handling vacuum-polarization loops and light-by-light-scattering loops, we have obtained fortran programs for 12 more subsets [ref] .
Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant · Introduction · 0.81
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