Electroweak two-loop corrections to sin2 θeff b(b)over-bar and Rb using numerical Mellin-Barnes integrals

Multi-loop integrals can be evaluated numerically using Mellin-Barnes representations. Here this technique is applied to the calculation of electroweak two-loop correction with closed fermion loops for two observables: the effective weak mixing angle for bottom quarks, sin(2) theta(b (b) over bar)(eff), and the branching ratio of the Z boson into bottom quarks, R-b. Good agreement with a previous result for sin(2) theta(b (b) over bar)(eff) is found. The result for R-b is new and it turns out that the electroweak two-loop corrections are relatively large - of the same order as the current experimental uncertainty. A simple parametrization formula is provided which approximates the full result within integration errors.