Mass and scheme effects in coupling constant evolution

We consider two theoretical aspects of coupling constant evolution: the details of effective coupling behavior in the threshold vicinity and the scheme dependence of the Grand Unification description. Our discussion is based on the Bogoliubov renorm-group formulation and particularly on a new analytic solution of a system of mass-dependent two-loop RG evolution equations for three effective couplings of the standard model. Accurate analysis of the threshold singularity reveals the effect connected with kinematic details of heavy particle creation resulting in an effective shift of the threshold mass $M\to M_*$. On the other hand, we demonstrate that the threshold crossing generally changes the subtraction scheme. This means that the appropriate choice of a subtraction scheme is important in discussing the unification criterion.