Tenth-Order Lepton Anomalous Magnetic Moment -- Second-Order Vertex Containing Two Vacuum Polarization Subdiagrams, One Within the Other

TL;DR

This paper calculates the tenth-order quantum electrodynamics contributions to the anomalous magnetic moments of electron and muon from complex vacuum polarization diagrams, providing precise numerical results and comparisons with analytic predictions.

Contribution

It presents the first detailed numerical evaluation of tenth-order diagrams with nested vacuum polarization loops, including mass-dependent effects, advancing precision in g-2 calculations.

Findings

Numerical results for electron g-2 contributions: 0.028597(4) (alpha/pi)^5.

Numerical results for muon g-2 contributions: 2.6409(4) (alpha/pi)^5.

Agreement with recent asymptotic analytic results for electron loops.

Abstract

This paper reports the tenth-order QED contribution to the g-2 of electron and muon from two gauge-invariant sets, Set I(g) and Set I(h). In the case of electron g-2 Set I(g) consists of 9 Feynman diagrams which have a 4th-order vacuum-polarization loop containing another 4th-order vacuum-polarization loop. Set I(h) consists of 30 Feynman diagrams which have a proper 6th-order vacuum-polarization loop containing a second-order vacuum-polarization loop. The results of numerical integration, including mass-dependent terms containing one closed loop of muon, are 0.028 597 (4) (alpha/pi)^5 for Set I(g) and 0.001 685 (13) (alpha/pi)^5 for Set I(h), respectively. We also report the contributions of Set I(g) and Set I(h) to the muon anomaly. Diagrams included are those containing electron, muon, and tau-lepton loops. Their sums are 2.640 9 (4) (alpha/pi)^5 and -0.564 8 (11) (alpha/pi)^5, respectively. The sum of contributions of Sets I(g) and I(h) containing only electron loops are in fair agreement with the recently obtained asymptotic analytic results.