On the electroweak contribution to the matching of the strong coupling constant in the SM

The effective renormalizable theory describing electromagnetic and strong interactions of quarks of five light flavors (nf=5nf=5QCD×QEDQCD×QED) is considered as a low-energy limit of the full Standard Model. Two-loop relation between the running strong coupling constants αsαs defined in either theories is found by simultaneous decoupling of electroweak gauge and Higgs bosons in addition to the top-quark. The relation potentially allows one to confront “low-energy” determination of αsαs with a high-energy one with increased accuracy. Numerical impact of new O(αsα)O(αsα) terms is studied at the MZMZ scale. It is shown that the corresponding contribution, although being suppressed with respect to O(αs2) terms, is an order of magnitude larger than the three-loop QCD corrections O(αs3) usually taken into account in four-loop renormalization group evolution of αsαs. The dependence on the matching scale is also analyzed numerically.