Subtractive procedure for calculating the anomalous electron magnetic moment in QED and its application for numerical calculation at the three-loop level

Volkov, S. N.

doi:10.1134/s1063776116050113

Cited by 13 publications

(76 citation statements)

References 50 publications

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“…including the ones containing lepton loops; see Ref. [44]. However, a rigorous mathematical proof for this fact is not developed even for graphs without lepton loops.…”

Section: Divergence Eliminationmentioning

confidence: 99%

“…It is easy to see this equivalence in the 2-loop case; see Section 3 of Ref. [44]. Let us note that we do not use the operator of QED on-shell renormalization of electron self-energy subgraphs; the Ward identity helps us in this case too.…”

mentioning

confidence: 97%

“…See the definition in Refs. [44,42]. 7 We consider only such subgraphs that are strongly connected and contain all lines that join the vertexes of the given subgraph.…”

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confidence: 99%

“…For a detailed explanation of the developed method, see Ref. [44] and some additional explanations in Refs. [42,32].…”

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confidence: 99%

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Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

Volkov

2019

Phys. Rev. D

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This paper describes a computation of a part of the QED contribution to the electron anomalous magnetic moment that was performed by the author with the help of a supercomputer. The computed part includes all 5-loop QED Feynman graphs without lepton loops. The calculation has led to the result A (10) 1 [no lepton loops] = 6.793(90) that is slightly different than the value 7.668(159) presented by T. Aoyama, T. Kinoshita, and M. Nio in 2018. The discrepancy is about 4.8σ . The computation gives the first independent check for that value. A shift in the fine-structure constant prediction is revealed in the paper. The developed calculation method is based on (a) a subtraction procedure for removing all ultraviolet and infrared divergences in Feynman parametric space before integration; (b) a nonadaptive Monte Carlo integration that uses the probability density functions that are constructed for each Feynman graph individually using its combinatorial structure. The method is described briefly in the paper (with the corresponding references to the previous papers). The values for the contributions of nine gauge-invariant classes splitting the whole set are presented in the paper. Moreover, the whole set of all 5-loop graphs without lepton loops is split into 807 subsets for comparison (in the future) of the calculated values with the values obtained by another methods. These detailed results are presented in the supplemental materials. Also, the supplemental materials contain the contribution values for each of 3213 individual Feynman graphs. An "oscillating" nature of these values is discussed. A realization of the numerical integration on the graphics accelerator NVidia Tesla V100 (as a part of the supercomputer "Govorun" from JINR, Dubna) is described with technical details such as pseudorandom generators, calculation speed, code sizes and structure, prevention of round-off errors and overflows, etc.

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“…including the ones containing lepton loops; see Ref. [44]. However, a rigorous mathematical proof for this fact is not developed even for graphs without lepton loops.…”

Section: Divergence Eliminationmentioning

confidence: 99%

mentioning

confidence: 97%

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Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

Volkov

2019

Phys. Rev. D

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“…The subtraction procedure was checked independently by F. Rappl using Monte Carlo integration based on Markov chains [38]. 4 Moreover, it can generate additional IR-divergences, see a more detailed explanation in [22]. 5 If G is a vertex-like (see section II.A) subgraph of a graph G , this subgraph contains the vertex that is incident to the external photon line of G , and the electron path connecting the external electron lines of G passes through G , then the Feynman amplitude of G is "enhanced" by an IR divergent multiplier, see [34,35].…”

Section: Feynman Parameters Can Be Used Directly Without Any Additiomentioning

confidence: 99%

New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED

Volkov

2017

Phys. Rev. D

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This paper presents a new method of numerical computation of the massindependent QED contributions to the electron anomalous magnetic moment which arise from Feynman graphs without closed electron loops. The method is based on a forest-like subtraction formula that removes all ultraviolet and infrared divergences in each Feynman graph before integration in Feynman-parametric space. The integration is performed by an importance sampling Monte-Carlo algorithm with the probability density function that is constructed for each Feynman graph individually. The method is fully automated at any order of the perturbation series. The results of applying the method to 2-loop, 3-loop, 4-loop Feynman graphs, and to some individual 5-loop graphs are presented, as well as the comparison of this method with other ones with respect to Monte Carlo convergence speed.

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Infrared and ultraviolet power counting on the mass shell in quantum electrodynamics

Volkov

2020

Nuclear Physics B

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Subtractive procedure for calculating the anomalous electron magnetic moment in QED and its application for numerical calculation at the three-loop level

Cited by 13 publications

References 50 publications

Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED

Infrared and ultraviolet power counting on the mass shell in quantum electrodynamics

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