Analytic contribution to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>factor of the electron in sixth order

LeVine, M. J.; Roskies, R.

doi:10.1103/physrevd.14.2191

Cited by 16 publications

(8 citation statements)

References 5 publications

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“…The vacuum polarization contribution [IS] is simply (2.12) The self-energy or vacuum fluctuation contribution (2.13) has had a more difficult history [16], but is now reliably given by = - The higher order magnetic moment contribution like (2.11), shifts all states and contributes to finestructure splitting, so we include both the fourth-order coefficient (2.16) and the sixth-order coefficient [17,5] a6= (;)3 [1.285±0.057]. (2.17) Somewhat better values are available [18], but the effect on the energy levels is negligible, so we will use the value (2.17) for uniformity with reference [S]. Althongh a6 gives a nearly negligible energy shift, it is.…”

Section: Quantum Electrodynamics Effectsmentioning

confidence: 99%

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Energy levels of one-electron atoms

Erickson

1977

Journal of Physical and Chemical Reference Data

382

182

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The table of precise one-electron atomic energy levels given by Garcia and Mack in 1965 is expanded to include' all atomic numbers and more energy levels, updated by using more recent values of fundamental constants and radiative corrections, and extended,to the maximum precision allowed by quantum electrodynamics (QED) calculations. All levels with n ~ 11 are given for Z ;;;2 15, wlrh n 2 5 for Z ;;;2 39, and with n;a; 3 for Z;a; 105. In addition, the SI/2 and Pl/2 and j=n-:-l/2 levels with n;a; 20 are given for z;a; 15, and with n;a; 13 for z;a; 39. The uncertainty in the QED calculations is given for each level. and the level is given to that precision. tonversions to different units and corrections for changing the Rydberg or nuclear mass values are pointed out. The paper includes a comprehensive bsting and brief discussions of all effects considered and of the uncertainties for the calculated and neglected terms. The Fine Structure Interval (difference between the j = I ± 1/2 levels for given nand l) and its reduced mass and QED contributions are discussed in detail. All known' measurements of Lamb shifts and other fine structure differences are compared with,calculated values"

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Section: Quantum Electrodynamics Effectsmentioning

confidence: 99%

“…the highest order term calculated in quantum electrodynamics and is directly tested by the measurement [19] is the "WQED" value [5] given by experiments that do not require quantum electrodynamics for their analyses. For a more recent comparison, see reference [18].…”

Section: Quantum Electrodynamics Effectsmentioning

confidence: 99%

Energy levels of one-electron atoms

Erickson

1977

Journal of Physical and Chemical Reference Data

382

182

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“…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%

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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“…A CUDA kernel is a GPU function that is called from the CPU part; see[48] 21. We are not sure that we understand the behavior of the NVidia optimizer.…”

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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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Analytic contribution to thegfactor of the electron in sixth order

Cited by 16 publications

References 5 publications

Energy levels of one-electron atoms

Energy levels of one-electron atoms

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

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