Freezing of alpha(s)(Q(2)) in e(+)e(-) annihilation

A new background-field formalism for QCD, exploiting nonperturbative background correlation functions as a dynamical input, is used to redefine alpha(s) in e(+)e(-) annihilation. The general result, found earlier for the static potential, that alpha(s)(Q(2)) is frozen at small Euclidean Q, alpha(s)(Q(2)) less than or equal to alpha(s)(max), is confirmed, and the estimate alpha(s)(max) = alpha(s)(Q(2) = 0) is expressed in terms of the physical hybrid-state mass M-B. The e(+)e(-) amplitude is described in the entire Euclidean region Q(2):0 less than or equal to Q(2) less than or similar to M-Z(2). The corresponding alpha(s)(Q(2)) is found to be frozen at the value of alpha(s)(Q(2) = 0) = 0.414 for M-B = 1.5 GeV, which is supported by a low-energy analysis by QCD sum rules. At the same time, a modified expression for alpha(s)(Q(2)) yields alpha(s)(M-tau) = 0.310 and alpha(s)(M-Z) = 0.120, and the corresponding values of Lambda are Lambda((5)) = 235 MeV, Lambda((4)) = 347 MeV, and Lambda((3)) = 427 MeV. Using the nonperturbative background formalism, we have also reformulated the sum-rule analysis of e(+)e(-) data and obtained a good description of experimental data with our alpha(s)(Q(2)).