Tord Riemann

Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0

We introduce the Mellin-Barnes representation of general Feynman integrals and discuss their evaluation. The Mathematica package AMBRE has been recently extended in order to cover consistently non-planar Feynman integrals with two loops. Prospects for the near future are outlined. This write-up is an introduction to new results which have also been presented elsewhere.

The two-loop electroweak bosonic corrections to sin2θeffb

The prediction of the effective electroweak mixing angle

30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Z

sin^2theta_{rm eff}^{rm b}

\bar b

in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the

b vertex

Z{bar b}b

Complete electroweak two-loop corrections to Z boson production and decay

vertex. Numerical predictions are presented in the form of a fitting formula as function of

Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

M_Z, M_W, M_H, m_t

Electroweak Bosonic 2-loop Corrections to the

and

Z

Delta{alpha}

-pole Precision Observables

,