Abstract
We re-examine the estimate of α s and of the QCD condensates from e + e − → I = 1 hadrons data. We conclude that e + e − at low energies gives a value of Λ compatible with the one from LEP and from tau inclusive decay. Using a τ-like inclusive process and QCD spectral sum rules, we estimate the size of the D = 4 to 9 condensates by a fitting procedure without invoking stability criteria. We find 〈 α s G 2〉 = (7.1 ± 0.7)10 −2 GeV 4, ϱα s〈 uu〉 2 = (5.8 ± 0.9)10 −4 GeV 6, which confirm previous sum rules estimate based on stability criteria. The corrections due to the D = 8 condensates and to instantons on the vector component of τ-decay are respectively δ 1 (8) = −(1.5 ± 0.6)10 −2( 1.78 M τ ) 8 and δ 1 (9) = −(7.0 ± 26.5)10 −4( 1.78 M τ ) 9 , which indicate that δ 1 (8) is one order magnitude higher than the vacuum saturation value, while the D ≥ 9 instanton-like contribution to the the vector component of the τ-decay width is a negligible correction. We also show that, due to the correlation between the D = 4 and 1 M τ 2 contributions in the ratio of the Laplace sum rules, the present value of the gluon condensate already excludes the recent estimate of the 1 M τ 2- term from FESR in the axial-vector channel. Combining our non-perturbative results with the resummed perturbative corrections to the τ-width R τ , we deduce from the present data α s ( M τ ) = 0.33 ± 0.03.
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