Numerical calculation of 5-loop QED contributions to the electron anomalous magnetic moment

Abstract

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: 1) a subtraction procedure for removing infrared (IR) and ultraviolet (UV) divergences point by point in Feynman parametric representation before integration; 2) 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; 3) a GPU-based numerical integration with the help of the supercomputer "Govorun" (JINR, Dubna, Russia).

preprint prepared for ACAT-2019 proceedings (and sent to Journal of Physics: Conference Series)

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Cited by in corpus (1)

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