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