Comment on the Dispersion Relations used to Calculate $\Delta \rho$

Abstract

We use the operator product expansion (OPE) to show that non-perturbative QCD corrections to $\Delta \rho$ can be calculated using unsubtracted dispersion relations for either the transverse or the longitudinal vacuum polarization functions. Recent calculations of the non-perturbative contribution to $\Delta \rho$ based on a non-relativistic calculation of corrections to the $\text{ttbar}$ threshold are inconsistent with this result.

Comments: 12 pgs of Latex. FERMILAB-PUB-94/037-T, EFI 94-07