Eur. Phys. J. C (2006) 46: 157-178
https://doi.org/10.1140/epjc/s2006-02478-9

Theoretical Physics

Evaluating massive planar two-loop tensor vertex integrals

¹ Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, 55099, Mainz, Germany
² Füüsika-Keemiateaduskond, Tartu Ülikool, Tähe 4, 51010, Tartu, Estonia

^* e-mail: groote@zino.physik.uni-mainz.de

Received: 14 September 2005
Revised: 2 December 2005
Published online: 9 March 2006

Abstract

Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones in the two-loop corrections necessary, for instance, for the decay of the Z⁰ boson. Instead of calculating particular decay processes, we present a new algorithm which allows us to perform arbitrary next-to-next-to-leading order (NNLO) calculations for massive planar two-loop vertex functions in the general mass case. All integration steps up to the last two are performed analytically and will be implemented under xloops as part of the Mainz xloops-GiNaC project. The last two integrations are done numerically using methods like VEGAS and Divonne. Thresholds originating from Landau singularities are found and discussed in detail. In order to demonstrate the numerical stability of our methods we consider particular Feynman integrals which contribute to different physical processes. Our results can be generalized to the case of the crossed topology.