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

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.