A contribution to sixth-order electron and muon anomalies. — III

Barbieri, Riccardo; Caffo, M.; Remiddi, E.

doi:10.1007/bf02763393

Cited by 13 publications

(8 citation statements)

References 6 publications

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“…High-order calculations in Quantum Field Theory require performing some operations with enormous amounts of information. For example, the total integrand code size 13 for A (8) 1 [no lepton loops] is 2.5 GB. There are too many places where a mistake can emerge.…”

Section: The Contribution Of Each Feynman Graph To a (2n)mentioning

confidence: 99%

“…2 The value for A (6) 1 was a product of efforts of many scientists. See, for example, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…in 64-bit in 80-bit precisions that are supported on processors that are compatible with Intel x86 family 10 See Section IV.B.11 See TableXVII.12 NVidia Tesla K80 has 2 GPUs 13. See TableXVII.…”

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confidence: 99%

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Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment

Volkov

2018

Phys. Rev. D

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Preliminary numerical results of calculating the 5-loop QED contributions to the electron (and muon) anomalous magnetic moment are presented. The results include the total contribution of the 5-loop Feynman diagrams without lepton loops and the contributions of nine gauge-invariant classes that form that set. A discrepancy with known results is revealed. The contributions of the gauge-invariant classes are presented for the first time. The method of the computation is briefly described (with the corresponding references). The calculation is based on the following elements:(i)a subtraction procedure for removing infrared (IR) and ultraviolet (UV) divergences point by point in Feynman parametric representation before integration; (ii)a nonadaptive Monte Carlo integration method that is founded on probability density functions (PDF) that are constructed for each Feynman diagram individually using its combinatorial structure; (iii)a GPU-based numerical integration with the help of the supercomputer "Govorun" (JINR, Dubna, Russia).

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Section: The Contribution Of Each Feynman Graph To a (2n)mentioning

confidence: 99%

“…2 The value for A (6) 1 was a product of efforts of many scientists. See, for example, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment

Volkov

2018

Phys. Rev. D

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“…That value was a product of efforts of many researchers; see, for example, Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. First numerical estimations for A were obtained by T. Kinoshita and W. B. Lindquist in 1981 and published in Ref.…”

Section: Introductionmentioning

confidence: 99%

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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“…The rules for this renormalization in the 3-loop case doesn't lead to an automated procedure at any order of perturbation. Simultaneously, approximately at the end of 1960s, the work of analytical calculation of A (6) 1 was started with help of computers (see [22][23][24][25][26][27][28][29][30][31][32][33] etc.). This work was finished in 1996 when in [33] the value A (6) 1 = 1.181241456 .…”

Section: Introductionmentioning

confidence: 99%

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

Volkov¹

2016

J. Exp. Theor. Phys.

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A new subtraction procedure for removal both ultraviolet and infrared divergences in Feynman integrals is proposed. This method is developed for computation of QED corrections to the electron anomalous magnetic moment. The procedure is formulated in the form of a forest formula with linear operators that are applied to Feynman amplitudes of UV-divergent subgraphs. The contribution of each Feynman graph that contains propagators of electrons and photons is represented as a finite Feynman-parametric integral. Application of the developed method to the calculation of 2-loop and 3-loop contributions is described.

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A contribution to sixth-order electron and muon anomalies. — III

Cited by 13 publications

References 6 publications

Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment

Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment

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

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

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