Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-08-29
JHEP 0110:009,2001
Physics
High Energy Physics
High Energy Physics - Phenomenology
38 pages, JHEP.cls,Changes: mistake in the calculations of the OPE coefficients corrected, numerical results: OPAL data discus
Scientific paper
10.1088/1126-6708/2001/10/009
Exact analytical expressions for the $\Delta S=1$ coupling $\im G_E$ in terms of observable spectral functions are given. This coupling determines the size of the $\Delta I=3/2$ contribution to $\epsilon'$. We show analytically how the scheme-dependence and scale dependences vanish to all orders in $1/N_c$ and NLO in $\alpha_S$ explicitly both for $Q_7$ and $Q_8$. Numerical results are derived for both $Q_7$ and $Q_8$ from the $\tau$-data and known results on the scalar spectral functions. In particular we study the effect of all higher dimension operators. The coefficients of the leading operators in the OPE of the needed correlators are derived to NLO in $\alpha_S$.
Bijnens Johan
Gamiz Elvira
Prades Joaquim
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