Tenth-order QED lepton anomalous magnetic moment: Eighth-order vertices containing a second-order vacuum polarization

Aoyama, T.; Hayakawa, Masashi; Kinoshita, T.; Nio, Makiko

doi:10.1103/physrevd.85.033007

Cited by 36 publications

(38 citation statements)

References 37 publications

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“…Thus far, the results of numerical evaluation of 31 gauge-invariant subsets, which consists of 6318 vertex diagrams, have been published [11][12][13][14][15][16][17][18][19][20]. The results of all 10 subsets of Set I, consisting of 208 vertex diagrams, have been confirmed by Ref.…”

Section: Introductionsupporting

confidence: 62%

“…Considerable numerical cancellation is expected among the nine terms on the lhs of Eq. (19). In fact the rhs exhibits the consequence of such a cancellation at the algebraic level.…”

Section: Reducing the Number Of Integralsmentioning

confidence: 99%

“…It is associated with the vanishing of V -function of the denominators in Eq. (20) in the integration domain characterized by [47,49] …”

Section: E Construction Of Ir Divergence Subtraction Termsmentioning

confidence: 99%

“…M n , n = 2, 4, · · · , refers to the magnetic moment projection of the sum of the set of unrenormalized vertex amplitudes transformed by means of the Ward-Takahashi identity (19), given in the form…”

Section: Separation Of Uv Divergences By K-operationmentioning

confidence: 99%

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Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops

et al. 2015

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This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726 (336)(α/π) 5 , which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795 (336)(α/π) 5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a e (theory) = 1 159 652 181.643 (25)(23)(16)(763) × 10 −12 , where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from α −1 = 137.035 999 049 (90), the fine-structure constant derived from the rubidium recoil measurement. Thus, a e (experiment) − a e (theory) = −0.91 (0.82) × 10 −12 .Assuming the validity of the standard model, we obtain the fine-structure constant α −1 (a e ) = 137.035 999 1570 (29)(27)(18)(331), where uncertainties are from the eighth-order term, tenthorder term, hadronic and electroweak terms, and the measurement of a e . This is the most precise value of α available at present and provides a stringent constraint on possible theories beyond the standard model.

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Section: Introductionsupporting

confidence: 62%

“…Considerable numerical cancellation is expected among the nine terms on the lhs of Eq. (19). In fact the rhs exhibits the consequence of such a cancellation at the algebraic level.…”

Section: Reducing the Number Of Integralsmentioning

confidence: 99%

“…It is associated with the vanishing of V -function of the denominators in Eq. (20) in the integration domain characterized by [47,49] …”

Section: E Construction Of Ir Divergence Subtraction Termsmentioning

confidence: 99%

Section: Separation Of Uv Divergences By K-operationmentioning

confidence: 99%

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Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops

et al. 2015

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“…We have also made a few runs for the 7-5 and 7-6 resultants (also taken from [30]) and find minima around 250 and 300 respectively. 3 This suggests that if the number of variables is in the range of 13 to 15 a good value for the number of expansions is 200-250. This number will then be multiplied by the number of runs of MCTS to obtain a indicative total number of tree expansions.…”

Section: Repeating Runs Of Mcts When C P Is Lowmentioning

confidence: 99%

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Herik

Kuipers

Vermaseren

et al. 2014

Communications in Computer and Information Science

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Abstract. After a computer chess program had defeated the human World Champion in 1997, many researchers turned their attention to the oriental game of Go. It turned out that the minimax approach, so successful in chess, did not work in Go. Instead, after some ten years of intensive research, a new method was developed: MCTS (Monte Carlo Tree Search), with promising results. MCTS works by averaging the results of random play-outs. At first glance it is quite surprising that MCTS works so well. However, deeper analysis revealed the reasons.The success of MCTS in Go caused researchers to apply the method to other domains. In this article we report on experiments with MCTS for finding improved orderings for multivariate Horner schemes, a basic method for evaluating polynomials. We report on initial results, and continue with an investigation into two parameters that guide the MCTS search. Horner's rule turns out to be a fruitful testbed for MCTS, allowing easy experimentation with its parameters. The results reported here provide insight into how and why MCTS works. It will be interesting to see if these insights can be transferred to other domains, for example, back to Go.

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Electromagnetic and Weak Radiative Corrections

Jegerlehner¹

2017

Springer Tracts in Modern Physics

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Tenth-order QED lepton anomalous magnetic moment: Eighth-order vertices containing a second-order vacuum polarization

Cited by 36 publications

References 37 publications

Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops

Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Electromagnetic and Weak Radiative Corrections

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