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}(eff,bb), and the branching ratio of the Z boson into bottom quarks, R(b). Good agreement with a previous result for sin^2{ \theta}(eff,bb) is found. The result for R(b) is new, and a simple parametrization formula is provided which approximates the full result within integration errors.
Categories: hep-ph