One-loop corrections at future linear colliders

Abstract

In order to benefit from high precision measurements at a future Linear Collider, we need to go beyond the tree level for cross section calculations in the electroweak sector. At the one-loop level, the number of Feynman diagrams has increased rapidly and the internal loops greatly complicate the calculations. Fortunately automated systems have been constructed to deal with these large scale computations. In particular, the GRACE system is capable of calculating general processes of up to four final particles including their masses.

In this report I will review some of the challenges that these automated systems meet and explain how to deal with them. Additionally, I will present my findings on the calculation of $e^+e^- \rightarrow Z Z H$ and $Z H H$ in order to study the couplings between the Higgs particles and the vector bosons in the standard model. The project will use the GRACE system for this and make a few additions to it. In particular a system to integrate over matrix elements that occupy more than 2 Gbytes in the computer. Because of numerical cancellations between the diagrams this is highly nontrivial.