Proper eighth-order vacuum-polarization function and its contribution to the tenth-order lepton g-2

Journal Article · Tue Mar 01 00:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.053003· OSTI ID:21578168

Aoyama, T ^[1]; Hayakawa, M ^[2]; Kinoshita, T ^[2]; Nio, M ^[2]

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1. Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602 (Japan)
2. Theoretical Physics Laboratory, Nishina Center, RIKEN, Wako, 351-0198 (Japan)

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 an electron loop to the electron g-2 is 0.017 47 (11)({alpha}/{pi}){sup 5}. The contribution of diagrams containing a muon loop is 0.000 001 67 (3)({alpha}/{pi}){sup 5}. The contribution of a tau-lepton loop is negligible at present. The sum of all these terms is 0.017 47 (11)({alpha}/{pi}){sup 5}. The contribution of diagrams containing an electron loop to the muon g-2 is 0.0871 (59)({alpha}/{pi}){sup 5}. This is to be compared with the unpublished asymptotic analytic result (0.252 37+O(m{sub e}/m{sub {mu}}))({alpha}/{pi}){sup 5}. The contribution of a tau-lepton loop to a{sub {mu}} is 0.000 237 (1)({alpha}/{pi}){sup 5}. The total contribution to a{sub {mu}}, the sum of these terms and the mass-independent term, is 0.1048 (59)({alpha}/{pi}){sup 5}.

• OSTI ID: 21578168
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevD.83.053003; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
ELECTRONS
EVALUATION
FEYNMAN DIAGRAM
FORTRAN
FUNCTIONS
GAUGE INVARIANCE
MAGNETIC MOMENTS
MASS
MUONS
TAU PARTICLES
VACUUM POLARIZATION
DIAGRAMS
ELEMENTARY PARTICLES
FERMIONS
HEAVY LEPTONS
INFORMATION
INVARIANCE PRINCIPLES
LEPTONS
MATHEMATICAL SOLUTIONS
PROGRAMMING LANGUAGES