Analytic QCD models are those versions of QCD in which the running coupling
parameter a(Q^2) has the same analytic properties as the spacelike physical
quantities, i.e., no singularities in the complex Q^2 plane except on the
timelike semiaxis. In such models, a(Q^2) usually differs from its perturbative
analog by power terms ~(Lambda^2/Q^2)^k for large momenta, introducing thus
nonperturbative terms in spacelike physical quantities whose origin is the UV
regime. Consequently, it contradicts the ITEP-OPE philosophy which states that
such terms can come only from the IR regimes. We investigate whether it is
possible to construct analytic QCD models which respect the ITEP-OPE philosophy
and, at the same time, reproduce not just the high-energy QCD observables, but
also the low-energy ones, among them the well-measured semihadronic tau decay
ratio.Comment: 33 pages, 13 figures, 7 tables; grammatical corrections in the text;
to appear in PR
