Three-loop topology analysis of neutral B-meson mixing with tapir

Abstract

Modern advances in particle physics depend strongly on the usage of reliable computer programs. In this context two issues become important: The usage of powerful algorithms to handle the amount of evaluated data properly, and a software architecture capable to overcome the problems of maintainability and extendability. We present our approach to such a computer program, called tapir. This tool assists computations in perturbative quantum field theory in many ways. Such calculations often involve the evaluation of a large amount of Feynman diagrams with multiple loops. tapir helps in reducing the number of diagrams, and the resulting integrals thereof, by identifying and minimizing their topological structure. We will focus on a three-loop calculation which is needed for the next-to-next-to leading order predictions of neutral $B$-meson systems. We show how tapir can be utilized for this kind of calculation.