A. Freitas, Yi-Cheng Huang
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 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.
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http://arxiv.org/abs/1205.0299
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