LEADING VACUUM-POLARIZATION CONTRIBUTIONS TO THE RELATION BETWEEN POLE AND RUNNING MASSES

Abstract

The vacuum--polarization contributions of ${\cal O}(b^{n-1} \al_s^n)$ to the relation between the pole--mass $M$ of a quark and the \MS parameter $\mh (M)$ are evaluated by a straightforward method. They are found to approximate very well the exact answer, known through ${\cal O}(\al_s^2)$, 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 $n\ge 3$ are also dominant, we evaluate $M_t/{\hat{m}}_t(M_t)$, compare the results with those of optimization methods, briefly discuss $M_b/\mh_b (M_b)$, and estimate the irreducible errors in the perturbative series. Implications for the electroweak amplitude $\Delta \rho$ are emphasized. An update of the QCD corrections to this amplitude, including an estimate of the theoretical error, is given.

27 pages, 1 figure and 5 tables all included in the text in a compressed ps file

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