Leading vacuum-polarization contributions to the relation between pole and running masses

The vacuum-polarization contributions of O( b^n-1 σ_sⁿ) to the relation between the pole-mass M of a quark and the overlineMS parameter m̂(M) are evaluated by a straightforward method. They are found to approximate very well the exact answer, known through O( α_s²), thus providing a simple physical interpretation. Results are also given for the cases when the vacuum-polarization contributions are defined by the pinch technique prescription and specific background field gauges. Assuming that the terms n ⩾ 3 are also dominant, we evaluate {M _t}/{m̂_t(M _t) }, compare the results with those of optimization methods, briefly discuss {M _b}/{m̂_b(M _b) }, and estimate the irreducible errors in the perturbative series. Implications for the electroweak amplitude Δϱ are emphasized. An update of the QCD corrections to this amplitude, including an estimate of the theoretical error, is given.