ON THE PRECISION OF THE COMPUTATION OF THE QCD CORRECTIONS TO ELECTROWEAK VACUUM POLARIZATIONS

We demonstrate that the dispersive computation of the threshold enhanc ements to heavy quark vacuum polarizations is unstable. Because of the slow convergence of the dispersion relations the result critically de pends on the intermediate energy region where the non-relativistic app roximation, intrinsic to threshold calculations, is invalid. We discus s other ambiguities precluding a reliable calculation of the threshold contribution to the vacuum polarizations. In the absence of a solutio n prudence should force one to assign an error to the radiative correc tions not far below the level of the perturbative O(alphaalpha(s)) con tributions. This may preclude the extraction of the Higgs mass from pr ecision measurements.