Electroweak two-loop corrections to sin^2θ(eff,bb) and R(b) using numerical Mellin-Barnes integrals
arXiv:1205.0299 · doi:10.1007/JHEP08(2012)050, 10.1007/JHEP05(2013)074, 10.1007/JHEP10(2013)044
Abstract
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^2θ(eff,bb), and the branching ratio of the Z boson into bottom quarks, R(b). Good agreement with a previous result for sin^2θ(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.
12 pages, 2 figures. V2: typos in eqs. (9)-(14) fixed; error in the treatment of the running bottom-quark mass corrected, resulting in small shifts of the results in Tabs. 3,4, Fig. 2, and eqs. (21),(23); conclusions unchanged. V3: bug in calculation of R(b) corrected, resulting in a sizable reduction of the size of the two-loop correction