On the b-quark running mass in QCD and the SM

We consider electroweak corrections to the relation between the running MS‾ mass mb of the b quark in the five-flavor QCD×QED effective theory and its counterpart in the Standard Model (SM). As a bridge between the two parameters, we use the pole mass Mb of the b quark, which can be calculated in both models. The running mass is not a fundamental parameter of the SM Lagrangian, but the product of the running Yukawa coupling yb and the Higgs vacuum expectation value. Since there exist different prescriptions to define the latter, the relations considered in the paper involve a certain amount of freedom. All the definitions can be related to each other in perturbation theory. Nevertheless, we argue in favour of a certain gauge-independent prescription and provide a relation which can be directly used to deduce the value of the Yukawa coupling of the b quark at the electroweak scale from its effective QCD running mass. This approach allows one to resum large logarithms ln⁡(mb/Mt) systematically. Numerical analysis shows that, indeed, the corrections to the proposed relation are much smaller than those between yb and Mb.