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

Abstract

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.

Electron and muon g−2 anomalies in general flavor conserving two-Higgs-doublet models

“…After an improved determination of the fine structure constant [1], a new anomaly has emerged [2] concerning the anomalous magnetic moment of the electron a e ¼ ðg e − 2Þ=2: there is a discrepancy among the experimental determination and the Standard Model (SM) prediction [3][4][5][6][7][8], δa e ≡ a Exp e − a SM e ¼ −ð8.7 AE 3.6Þ × 10 −13 : ð1Þ…”

g−2 of charged leptons, α(MZ2) , and the hyperfine splitting of muonium

“…Note that very recently an independent calculation of the purely photonic five-loop contributions to a e was performed[15], which gives a different value compared to the one in Ref [11]. and which, if adopted, would slightly change the predictions for a SM e and Δa e .…”

Muon g − 2 vs LHC Run 2 in supersymmetric models

“…Since the electroweakinos are mixtures of the bino, wino, and higgsino gauge eigenstates, the production cross sections and the decay patterns are determined by the mixing composition and thus dependent on the parameters in Eq. (11). This is contrasted to typical setups in analyses of the ATLAS and CMS collaborations.…”

“…#1 It was reported [11] that an independent estimation of the purely photonic five-loop contribution to ae became inconsistent with the result of Ref. [2].…”