Abstract
This paper describes a method of numerical evaluating high-order QED contributions to the electron anomalous magnetic moment. The method is based on subtraction of infrared and ultraviolet divergences in Feynman-parametric space before integration and on nonadaptive Monte Carlo integration that is founded on Hepp sectors. A realization of the method on the graphics accelerator NVidia Tesla K80 is described. A method of removing round-off errors that emerge due to numerical subtraction of divergences without losing calculation speed is presented. The results of applying the method to all 2-loop, 3-loop, 4-loop QED Feynman graphs without lepton loops are presented. A detailed comparison of the 2-loop and 3-loop results with known analytical ones is given in the paper. A comparison of the contributions of 6 gauge invariant 4-loop graph classes with known analytical values is presented. Moreover, the contributions of 78 sets of 4-loop graphs for comparison with the direct subtraction on the mass shell are presented. Also, the contributions of the 5-loop and 6-loop ladder graphs are given as well as a comparison of these results with known analytical ones. The behavior of the generated Monte Carlo samples is described in detail, a method of the error estimation is presented. A detailed information about the graphics processor performance on these computations and about the Monte Carlo convergence is given in the paper.
Highlights
The electron anomalous magnetic moment (AMM) is known with a very high accuracy
The contributions of six gauge-invariant classes of 4-loop graphs without lepton loops are presented in Sec
Obtained interval 1⁄2y−; yþ does not satisfy the condition yþ − y− ≤ σ=4, where σ is the current error estimation44 for the obtained integral value, we repeat the calculation in the direct double-precision interval arithmetic
Summary
The electron anomalous magnetic moment (AMM) is known with a very high accuracy. In Ref. [1], the value ae 1⁄4 0.00115965218073ð28Þ was obtained. This procedure eliminates IR and UV divergences in each AMM Feynman graph point by point, before integration, in the spirit of Refs. The numerical subtraction of divergences leads to a situation in which small numbers (in absolute value) are obtained as the difference of astronomically big numbers This generates round-off errors that significantly affect the result.. The total number of 269 Feynman graphs for Að18Þ1⁄2no lepton loops is divided into 78 sets, and the contribution of each set must coincide with the contribution that is obtained by direct subtraction on the mass shell in Feynman gauge. The contributions of six gauge-invariant classes of 4-loop graphs without lepton loops are presented in Sec. IV H and compared with the semianalytical ones from Ref.
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