Tenth-order QED contribution to the lepton anomalous magnetic moment: Sixth-order vertices containing an internal light-by-light-scattering subdiagram

• Published in: Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2012-05, Vol.85 (9), Article 093013
• Main Authors: Aoyama, Tatsumi, Hayakawa, Masashi, Kinoshita, Toichiro, Nio, Makiko
• Format: Article
• Language: English
• Subjects: Cosmology; Gravitation; Leptons; Magnetic moment; Muons
• ISSN: 1550-7998; 1550-2368
• DOI: 10.1103/PhysRevD.85.093013

This paper reports the tenth-order QED contribution to the lepton g - 2 from the gauge-invariant set, called Set III(c), which consists of 390 Feynman vertex diagrams containing an internal fourth-order light-by-light-scattering subdiagram. The mass-independent contribution of Set III(c) to the electron g - 2 ( alpha sub(e)) is 4.9210 (103) in units of ( alpha /[pi]) super(5). The mass-dependent contributions to alpha sub(e) from diagrams containing a muon loop is 0.00370 (37) ( alpha /[pi]) super(5). The tau-lepton loop contribution is negligible at present. Altogether the contribution of Set III(c) to alpha sub(e) is 4.9247 (104) ( alpha /[pi]) super(5). We have also evaluated the contribution of the closed electron loop to the muon g - 2 ( alpha sub( mu )). The result is 7.435 (134) ( alpha /[pi]) super(5). The contribution of the tau-lepton loop to alpha sub( mu ) is 0.1999 (28) ( alpha /[pi]) super(5). The total contribution of various leptonic loops (electron, muon, and tau-lepton) of Set III(c) to alpha sub( mu ) is 12.556 (135)( alpha /[pi]) super(5).