On the relation between the fermion pole mass and $\overline{MS}$ Yukawa coupling in the standard model

We present the full one-loop correction to the relation between the running MSbar Yukawa coupling, $\overline h_f(\mu)$, at some renormalization scale, $\mu$, and the pole mass, $m_f$, of a fermion, $f$, in the standard model. Our result complements previous analyses that included just the QCD correction to this relation in the case of quarks. This allows us to convert, without loss of information, the threshold value, $\overline h_f(m_f)$, of $\overline h_f(\mu)$, which satisfies a renormalization-group equation and may be driven up to some high-energy scale of new physics, to physical observables at low energy. We investigate the limit of the Higgs boson and/or the top quark being much heavier than all the other particles. We also list simple and yet rather precise approximation formulae, which are convenient for applications