Tenth-Order Lepton Anomalous Magnetic Moment -- Sixth-Order Vertices Containing Vacuum-Polarization Subdiagrams

TL;DR

This paper calculates tenth-order contributions to the electron and muon g-2 from complex Feynman diagrams, using two methods that agree well, providing precise theoretical values for lepton magnetic moments.

Contribution

It introduces a new automatic code generation scheme for evaluating high-order Feynman diagrams, improving accuracy and efficiency in quantum electrodynamics calculations.

Findings

Contributions to electron g-2 are approximately 2.1273 and 3.3271 in units of (alpha/pi)^5.

Total contributions to muon g-2 from these diagrams are 112.418 and 15.407 in units of (alpha/pi)^5.

Results agree between two evaluation methods within numerical uncertainties.

Abstract

This paper reports the values of contributions to the electron g-2 from 300 Feynman diagrams of the gauge-invariant Set III(a) and 450 Feynman diagrams of the gauge-invariant Set III(b). The evaluation is carried out in two versions. Version A is to start from the sixth-order magnetic anomaly M_6 obtained in the previous work. The mass-independent contributions of Set III(a) and Set III(b) are 2.1275 (2) and 3.3271 (6) in units of (alpha/pi)^5, respectively. Version B is based on the recently-developed automatic code generation scheme. This method yields 2.1271 (3) and 3.3271 (8) in units of (alpha/pi)^5, respectively. They are in excellent agreement with the results of the first method within the uncertainties of numerical integration. Combining these results as statistically independent we obtain the best values, 2.1273 (2), and 3.3271 (5) times (alpha/pi)^5, for the mass-independent contributions of the Set III(a) and Set III(b), respectively. We have also evaluated mass-dependent contributions of diagrams containing muon and/or tau-particle loop. Including them the total contribution of Set III(a) is 2.1349 (2) and that of Set III(b) is 3.3299 (5) in units of (alpha/pi)^5. The total contributions to the muon g-2 of various leptonic vacuum-polarization loops of Set III(a) and Set III(b) are 112.418 (32) and 15.407 (5) in units of (alpha/pi)^5, respectively.