Tenth-Order QED contribution to Lepton Anomalous Magnetic Moment - Fourth-Order Vertices Containing Sixth-Order Vacuum-Polarization Subdiagrams

TL;DR

This paper calculates tenth-order quantum electrodynamics (QED) contributions to the anomalous magnetic moments of electrons and muons, focusing on specific Feynman diagram sets involving vacuum polarization, providing precise numerical results.

Contribution

It presents the first detailed evaluation of tenth-order QED contributions from gauge-invariant diagram sets with sixth-order vacuum polarization insertions.

Findings

Calculated contributions to electron g-2 from Set II(c) and II(d).

Calculated contributions to muon g-2 from Set II(c) and II(d).

Provided numerical values with uncertainties for all contributions.

Abstract

This paper reports the tenth-order contributions to the g-2 of the electron a_e and those of the muon a_mu from the gauge-invariant Set II(c), which consists of 36 Feynman diagrams, and Set II(d), which consists of 180 Feynman diagrams. Both sets are obtained by insertion of sixth-order vacuum-polarization diagrams in the fourth-order anomalous magnetic moment. The mass-independent contributions from Set II(c) and Set II(d) are -0.116 489 (32)(alpha/pi)^5 and -0.243 00 (29)(alpha/pi)^5, respectively. The leading contributions to a_mu, which involve electron loops only, are -3.888 27 (90)(alpha/pi)^5 and 0.4972 (65)(alpha/pi)^5 for Set II(c) and Set II(d), respectively. The total contributions of the electron, muon, and tau-lepton loops to a_e are -0.116 874 (32) (alpha/pi)^5 for Set II(c) and -0.243 10 (29) (alpha/pi)^5 for Set II(d). The contributions of electron, muon, and tau-lepton loops to a_mu are -5.5594 (11) (alpha/pi)^5 for Set II(c) and 0.2465 (65) (alpha/pi)^5 for Set II(d).