Automated calculation scheme for αn contributions of QED to lepton g−2: New treatment of infrared divergence for diagrams without lepton loops

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.