Comment on the Dispersion Relations used to Calculate $Δρ$

We use the operator product expansion (OPE) to show that non-perturbative QCD corrections to $Δρ$ 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 $Δρ$ based on a non-relativistic calculation of corrections to the $\ttbar$ threshold are inconsistent with this result.

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