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Exact analytical expressions for the $\Delta S=1$ coupling $\im G_E$ in termsof observable spectral functions are given. This coupling determines the sizeof the $\Delta I=3/2$ contribution to $\epsilon'$. We show analytically how thescheme-dependence and scale dependences vanish to all orders in $1/N_c$ and NLOin $\alpha_S$ explicitly both for $Q_7$ and $Q_8$.  Numerical results are derived for both $Q_7$ and $Q_8$ from the $\tau$-dataand known results on the scalar spectral functions. In particular we study theeffect of all higher dimension operators.  The coefficients of the leading operators in the OPE of the neededcorrelators are derived to NLO in $\alpha_S$.Comment: 38 pages, JHEP.cls,Changes: mistake in the calculations of the OPE  coefficients corrected, numerical results: OPAL data discussed more  extensively and analysis of ALEPH data extended and comparison with earlier  work rewritte

Matching the electroweak penguins Q7,Q8 and spectral correlators

Matching the electroweak penguins Q₇,Q₈ and spectral correlators