Automated Calculation Scheme for alpha^n Contributions of QED to Lepton g-2: New Treatment of Infrared Divergence for Diagrams without Lepton Loops

TL;DR

This paper introduces an efficient algorithm to handle infrared divergences in QED calculations of lepton g-2, enabling automated evaluation of complex diagrams without lepton loops, including those with infrared divergences.

Contribution

The authors developed a new subtraction algorithm integrated into an automated system to evaluate infrared-divergent QED diagrams without lepton loops, extending previous methods.

Findings

Successfully verified the system for sixth- and eighth-order cases.

Produced finite integrals for all q-type diagrams, including those with self-energy subdiagrams.

Currently evaluating over 6000 diagrams for tenth-order lepton g-2.

Abstract

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.