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

The vacuum-polarization contributions of O(b(n-1)alpha(s)(n)) to the r elation between the pole-mass M of a quark and the ($$$) over bar MS p arameter ($) over cap m(M) are evaluated by a straightforward method. They are found to approximate very well the exact answer, known throug h O(alpha(s)(2)), thus providing a simple physical interpretation. Res ults are also given for the cases when the vacuum-polarization contrib utions are defined by the pinch technique prescription and specific ba ckground field gauges. Assuming that the terms n greater than or equal to 3 are also dominant, we evaluate M(t)/($) over cap m(t)(M(t)), com pare the results with those of optimization methods, briefly discuss M (b)/($) over cap m(b)(M(b)), and estimate the irreducible errors in th e perturbative series. Implications for the electroweak amplitude Delt a rho are emphasized. An update of the QCD corrections to this amplitu de, including an estimate of the theoretical error, is given.