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

Understand

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.