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

Volkov, S. N.

doi:10.1103/physrevd.96.096018

Cited by 25 publications

(50 citation statements)

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“…[35] is consistent with both of preceding results (9) and (10). The contribution to A ð8Þ 1 from the 518 vertex diagrams without a fermion loop has also been independently cross-checked by using numerical means [36].…”

Section: Introductionsupporting

confidence: 88%

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Revised and improved value of the QED tenth-order electron anomalous magnetic moment

2018

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In order to improve the theoretical prediction of the electron anomalous magnetic moment a e we have carried out a new numerical evaluation of the 389 integrals of Set V, which represent 6,354 Feynman vertex diagrams without lepton loops. During this work, we found that one of the integrals, called X024, was given a wrong value in the previous calculation due to an incorrect assignment of integration variables. The correction of this error causes a shift of −1.26 to the Set V contribution, and hence to the tenth-order universal (i.e., mass-independent) term A1 . The previous evaluation of all other 388 integrals is free from errors and consistent with the new evaluation. Combining the new and the old (excluding X024) calculations statistically, we obtain 7.606ð192Þðα=πÞ 5 as the best estimate of the Set V contribution. Including the contribution of the diagrams with fermion loops, the improved tenth-order universal term becomes A ð10Þ 1 ¼ 6.675ð192Þ. Adding hadronic and electroweak contributions leads to the theoretical prediction a e ðtheoryÞ ¼ 1159652182.032ð720Þ × 10 −12 . From this and the best measurement of a e , we obtain the inverse fine-structure constant α −1 ða e Þ ¼ 137.0359991491ð331Þ. The theoretical prediction of the muon anomalous magnetic moment is also affected by the update of QED contribution and the new value of α, but the shift is much smaller than the theoretical uncertainty.

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Section: Introductionsupporting

confidence: 88%

“…Their values are given in Refs. [36,37]. We have compressed all 6,354 vertex diagrams to 389 integrals by certain algebraic manipulation.…”

Section: Introductionmentioning

confidence: 99%

Revised and improved value of the QED tenth-order electron anomalous magnetic moment

2018

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“…A good upper bound can play the role of a good probability density function for Monte Carlo integration; see Ref. [42]. However, in the real case we should use a more complicated formulas for obtaining Deg(s) .…”

Section: Monte Carlo Integration a Probability Density Functionsmentioning

confidence: 99%

“…We use the techniques for prevention of occasional emergence of very large values that are described in [42] (with little modifications and adaptation for GPU parallelism).…”

Section: A Evaluation Of the Integrands With Gpusmentioning

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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Application of the Continuous Stern Gerlach Effect: Magnetic Moments

Vogel

2024

Springer Series on Atomic, Optical, and Plasma Physics

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

Cited by 25 publications

References 50 publications

Revised and improved value of the QED tenth-order electron anomalous magnetic moment

Revised and improved value of the QED tenth-order electron anomalous magnetic moment

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

Application of the Continuous Stern Gerlach Effect: Magnetic Moments

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