In Search of the Breakdown of QED: Study of Lepton g - 2 from 1947 to Present
Abstract
This article is a revised and expanded version of a talk presented at the Third International Symposium on Lepton Moments, Cape Cod, June 19 - 22, 2006. It is expanded considerably to provide a historical perspective on the study of lepton g - 2, focusing on the numerical integration method which consists of two steps: (1) Analytic construction of FORTRAN codes of renormalized amplitudes for the lepton g - 2. (2) Numerical evaluation of the codes obtained in step (1). A systematic formulation was developed by 1974 to deal with the sixth-order case, later extended to the eighth-order case. To handle the far more complicated tenth-order case, we developed an algorithm that enables us to automatically construct fully renormalized FORTRAN codes representing a large fraction of 12672 Feynman diagrams. While applying this automation code to the eighth-order ae for the purpose of debugging, we found an inconsistency in the previous handling of linear infrared divergence. With this error corrected we now have two independent evaluations of the eighth-order term of ae, which agree with each other within the estimated uncertainty of numerical integration. The possible existence of further algebraic error, which might have eluded detection being smaller than the uncertainty of numerical integration, is eliminated by an extensive test evaluation of the integrands (not integrals themselves) in double precision, which shows that the old and new integrands agree to the first 15 digits at arbitrarily chosen points in the domain of integration. The current status of the calculation of the muon g - 2 is reviewed briefly. Numerical evaluation of the tenth-order ae is in an advanced stage.
- Publication:
-
Lepton Dipole Moments. Edited by ROBERTS B LEE ET AL. Published by World Scientific Publishing Co. Pte. Ltd
- Pub Date:
- 2010
- DOI:
- 10.1142/9789814271844_0003
- Bibcode:
- 2010ldm..book...69K