RIKEN-TH 182 arXiv:1001.3704v2 [hep-ph] 11 Mar 2010 Tenth-order lepton g − 2 : Contribution from diagrams containing a sixth-order light-by-light-scattering subdiagram internally Tatsumi Aoyama, 1 Katsuyuki Asano, 2 Masashi Hayakawa, 2 Toichiro Kinoshita, 3 Makiko Nio, 4 and Noriaki Watanabe 2 $^{1}$Faculty of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan $^{2}$Department of Physics, Nagoya University, Nagoya, Aichi 464-8602, Japan $^{3}$Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, New York 14853, USA $^{4}$Theoretical Physics Laboratory, Nishina Center, RIKEN, Wako, 351-0198, Japan (Dated: October 8, 2018) 1 Abstract This paper reports the result of our evaluation of the tenth-order QED correction to the lepton g − 2 from Feynman diagrams which have sixth-order light-by-light-scattering subdiagrams, none of whose vertices couple to the external magnetic field. The gauge-invariant set of these diagrams, called Set II(e), consists of 180 vertex diagrams. In the case of the electron g − 2 ( a$_{e}$ ), where the light-by-light subdiagram consists of the electron loop, the contribution to a$_{e}$ is found to be − 1 . 344 9 (10) ( α/π ) $^{5}$. The contribution of the muon loop to a$_{e}$ is − 0 . 000 465 (4) ( α/π ) $^{5}$. The contribution of the tau-lepton loop is about two orders of magnitudes smaller than that of the muon loop and hence negligible. The sum of all of these contributions to a$_{e}$ is − 1 . 345 (1) ( α/π ) $^{5}$. We have also evaluated the contribution of Set II(e) to the muon g − 2 ( a$_{µ}$ ). The contribution to a$_{µ}$ from the electron loop is 3 . 265 (12) ( α/π ) $^{5}$, while the contribution of the tau-lepton loop is − 0 . 038 06 (13) ( α/π ) $^{5}$. The total contribution to a$_{µ}$ , which is the sum of these two contributions and the mass-independent part of a$_{e}$ , is 1 . 882 (13) ( α/π ) $^{5}$. PACS numbers: 13.40.Em,14.60.Cd,14.60Ef,12.20.Ds