Proper Eighth-Order Vacuum-Polarization Function and its Contribution to the Tenth-Order Lepton g-2

TL;DR

This paper presents a detailed calculation of the eighth-order vacuum-polarization function and its precise contribution to the tenth-order lepton g-2, using advanced numerical methods and automated code generation.

Contribution

It introduces a new Feynman-parametric representation for eighth-order vacuum polarization and computes its contribution to lepton g-2 with high precision using automated code generation.

Findings

Electron loop contribution to electron g-2: 0.01747(11) (alpha/pi)^5

Muon loop contribution to muon g-2: 0.0871(59) (alpha/pi)^5

Total contribution to muon g-2: 0.1048(59) (alpha/pi)^5

Abstract

This paper reports the Feynman-parametric representation of the vacuum-polarization function consisting of 105 Feynman diagrams of the eighth order, and its contribution to the gauge-invariant set called Set I(i) of the tenth-order lepton anomalous magnetic moment. Numerical evaluation of this set is carried out using FORTRAN codes generated by an automatic code generation system gencodevpN developed specifically for this purpose. The contribution of diagrams containing electron loop to the electron g-2 is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing muon loop is 0.000 001 67 (3) (alpha/pi)^5. The contribution of tau-lepton loop is negligible at present. The sum of all these terms is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing electron loop to the muon g-2 is 0.087 1 (59) (alpha/pi)^5. That of tau-lepton loop is 0.000 237 (1) (alpha/pi)^5. The total contribution to a_mu, the sum of these terms and the mass-independent term, is 0.104 8 (59) (alpha/pi)^5.