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Multi-loop integrals can be evaluated numerically using Mellin-Barnesrepresentations. Here this technique is applied to the calculation ofelectroweak two-loop correction with closed fermion loops for two observables:the effective weak mixing angle for bottom quarks, sin^2{\theta}(eff,bb), andthe branching ratio of the Z boson into bottom quarks, R(b). Good agreementwith 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 thefull result within integration errors.

Electroweak two-loop corrections to sin^2{\theta}(eff,bb) and R(b) using numerical Mellin-Barnes integrals