Exact non-factorizable O(alpha_s g^2) two-loop contribution to Z -> b   bbar
  For Z -> b bbar, we calculate all the two-loop top dependent Feynman graphs, which have mixed QCD and electroweak contributions that are not factorizable. For evaluating the graphs, without resorting to a mass expansion, we apply a two-loop extension of the one-loop Passarino-Veltman reduction. This is an analytic-numerical method, which first converts all diagrams into a set of ten standard scalar functions, and then integrates them numerically over the remaining Feynman parameters, with rapid convergence and high accuracy. We discuss the treatment of infrared singularities within our methods. We do not resort to unitarity cuts of two-point functionsfor calculating decay rates; these are useful only to obtain an inclusive rate. For this reason, experimental cuts and the experimental infrared energy resolution can be implemented in our calculation, once the corresponding one-loop gluon Bremsstrahlung process is added to this calculation. 
Adrian Ghinculov, York-Peng Yao