The R ratio in e+ e-, the determination of alpha(Mz^2) and a possible non-perturbative gluonic contribution

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Abstract
We review the determination of the QED coupling at the Z pole, which is a crucial parameter for electroweak theory. We include recent e+e- -> hadron data from Novosibirsk and Beijing to re-evaluate alpha (M_Z^2). We find 1/alpha (M_Z^2) = 128.973 +/- 0.035 or 128.934 +/- 0.040 according, respectively, to whether inclusive or exclusive e+e- -> hadron data are used in the interval 1.4 < \sqrt{s} < 2.1 GeV. The error is mainly due to uncertainties in the data in the low energy region, \sqrt{s} < 2.5 GeV. We find that no advantage is obtained by analytic continuation of the dispersion relation into the complex s plane. We show that the hints of structure for \sqrt{s} ~ 2.5 GeV may be evidence of a non-perturbative gluonic contribution to R(s).

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