On the \(b\)-quark running mass in QCD and the SM. (English) Zbl 1356.81211

Bednyakov, A. V.; Kniehl, B. A.; Pikelner, A. F.; Veretin, O. L.

Nucl. Phys., B 916, 463-483 (2017).

Summary: We consider electroweak corrections to the relation between the running \(\overline{\mathrm{MS}}\) mass \(m_b\) of the \(b\) quark in the five-flavor \(\mathrm{QCD} \times \mathrm{QED}\) effective theory and its counterpart in the Standard Model (\(\mathrm{SM}\)). As a bridge between the two parameters, we use the pole mass \(M_b\) of the \(b\) quark, which can be calculated in both models. The running mass is not a fundamental parameter of the \(\mathrm{SM}\) Lagrangian, but the product of the running Yukawa coupling \(y_b\) 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 \(\ln(m_b / M_t)\) systematically. Numerical analysis shows that, indeed, the corrections to the proposed relation are much smaller than those between \(y_b\) and \(M_b\).

MSC:

81V05	Strong interaction, including quantum chromodynamics
81V22	Unified quantum theories
81V15	Weak interaction in quantum theory
81T15	Perturbative methods of renormalization applied to problems in quantum field theory

Software:

mr; RunDec

References:

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