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We consider electroweak corrections to the relation between the running $overline{mathrm{MS}}$ mass $m_b$ of the $b$ quark in the five-flavor QCD$times$QED effective theory and its counterpart in the Standard Model (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 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 favor 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 $M_b$.
We present the first two-loop calculation of the heavy quark energy shift in lattice nonrelativistic QCD (NRQCD). This calculation allow us to extract a preliminary prediction of $m_b(m_b, n_f = 5) = 4.25(12)$ GeV for the mass of the b quark from lat
We perform a benchmark study of the step scaling procedure for the ratios of renormalization constants extracted from position space correlation functions. We work in the quenched approximation and consider the pseudoscalar, scalar, vector and axial
Combined HERA data on charm production in deep-inelastic scattering have previously been used to determine the charm-quark running mass $m_c(m_c)$ in the MSbar renormalisation scheme. Here, the same data are used as a function of the photon virtualit
We calculate the radiative corrections to the nonleptonic inclusive B decay mode $brightarrow cbar u d$ taking into account the charm quark mass. Compared to the massless case, corrections resulting from a nonvanishing c quark mass increase the nonle
We calculate the lattice quark propagator in Coulomb gauge both from dynamical and quenched configurations. We show that in the continuum limit both the static and full quark propagator are multiplicatively renormalizable. From the propagator we extr