This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a_e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value
of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726(336)(alpha/pi)^5, which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795(336)(alpha/pi)^5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a_e(theory)=1 159 652 181.643(25)(23)(16)(763) times 10^{-12}, where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from alpha^{-1}=137.035 999 049(90), the fine-structure constant derived from the rubidium recoil measurement. Thus, a_e(experiment) - a_e(theory)= -0.91(0.82) times 10^{-12}. Assuming the validity of the standard model, we obtain the fine-structure constant alpha^{-1}(a_e)=137.035 999 1570(29)(27)(18)(331), where uncertainties are from the eighth-order term, tenth-order term, hadronic and electroweak terms, and the measurement of a_e. This is the most precise value of alpha available at present and provides a stringent constraint on possible theories beyond the standard model.
This paper reports the tenth-order QED contribution to lepton g-2 from diagrams of three gauge-invariant sets VI(d), VI(g), and VI(h), which are obtained by including various fourth-order radiative corrections to the sixth-order g-2 containing light-
by-light-scattering subdiagrams. In the case of electron g-2, they consist of 492, 480, and 630 vertex Feynman diagrams, respectively. The results of numerical integration, including mass-dependent terms containing muon loops, are 1.8418(95) (alpha/pi)^5 for the Set VI(d), -1.5918(65) (alpha/pi)^5 for the Set VI(g), and 0.1797(40) (alpha/pi)^5 for the Set VI(h), respectively. We also report the contributions to the muon g-2, which derive from diagrams containing an electron, muon or tau lepton loop: Their sums are -5.876(802) (alpha/pi)^5 for the Set VI(d), 5.710(490) (alpha/pi)^5 for the Set VI(g), and -8.361(232) (alpha/pi)^5 for the Set VI(h), respectively.
We have developed an efficient algorithm for the subtraction of infrared divergences that arise in the evaluation of QED corrections to the anomalous magnetic moment of lepton (g-2). By incorporating this new algorithm, we have extended the automated
code-generating system developed previously to deal with diagrams without internal lepton loops (called q-type), which produced convergent integrals when applied to diagrams that have only ultraviolet-divergent subdiagrams of vertex type. The new system produces finite integrals for all q-type diagrams, including those that contain self-energy subdiagrams and thus exhibit infrared-divergent behavior. We have thus far verified the system for the sixth- and eighth-order cases. We are now evaluating 6354 vertex diagrams of q-type that contribute to the tenth-order lepton g-2.
