Automatic calculation of two-loop ELWK corrections to the muon ($g$-2)

TL;DR

This paper presents an automated approach to calculating two-loop electroweak corrections to the muon g-2 using the GRACE-FORM system, incorporating gauge checks and advanced numerical techniques for precise results.

Contribution

The authors develop an automated method for two-loop electroweak correction calculations, extending existing systems with gauge checks and novel numerical regularization techniques.

Findings

Successful automatic calculation of 1780 two-loop diagrams.

Verification of divergence cancellations and gauge independence.

Implementation of advanced numerical methods for finite value extraction.

Abstract

Two-loop electroweak corrections to the muon anomalous magnetic moment are automatically calculated by using GRACE-FORM system, as a trial to extend our system for two-loop calculation. We adopt the non-linear gauge (NLG) to check the reliability of our calculation. In total 1780 two-loop diagrams consisting of 14 different topological types and 70 one-loop diagrams composed of counter terms are calculated. We check UV- and IR-divergences cancellation and the independence of the results from NLG parameters. As for the numerical calculation, we adopt trapezoidal rule with Double Exponential method (DE). Linear extrapolation method (LE) is introduced to regularize UV- and IR- divergence and to get finite values.