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

T. Aoyama1,2, M. Hayakawa2,3, T. Kinoshita2,4, and M. Nio2

  • 1Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602, Japan
  • 2Theoretical Physics Laboratory, Nishina Center, RIKEN, Wako, 351-0198, Japan
  • 3Department of Physics, Nagoya University, Nagoya, 464-8602, Japan
  • 4Laboratory for Elementary Particle Physics, Cornell University, Ithaca, New York, 14853, USA

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Phys. Rev. D 83, 053003 – Published 7 March, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.053003

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 This is to be compared with the unpublished asymptotic analytic result (0.252 37+O(me/mμ))(α/π)5.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

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See Also

Tenth-order QED contribution to lepton anomalous magnetic moment: Fourth-order vertices containing sixth-order vacuum-polarization subdiagrams

Tatsumi Aoyama, Masashi Hayakawa, Toichiro Kinoshita, and Makiko Nio
Phys. Rev. D 83, 053002 (2011)

Article Text

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Information

Phys. Rev. D 83, 053003– Published 7 March, 2011
  • Received 12 January 2011
Article part of CHORUS

© 2011 American Physical Society

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