  In contrast to perturbative QCD, the analytic QCD models have running
coupling whose analytic properties correctly mirror those of spacelike
observables. The discontinuity (spectral) function of such running coupling is
expected to agree with the perturbative case at large timelike momenta;
however, at low timelike momenta it is not known. In the latter regime, we
parametrize the unknown behavior of the spectral function as a sum of (two)
delta functions; while the onset of the perturbative behavior of the spectral
function is set to be 1.0-1.5 GeV. This is in close analogy with the "minimal
hadronic ansatz" used in the literature for modeling spectral functions of
correlators. For the running coupling itself, we impose the condition that it
basically merges with the perturbative coupling at high spacelike momenta. In
addition, we require that the well-measured nonstrange semihadronic (V+A) tau
decay ratio value be reproduced by the model. We thus obtain a QCD framework
which is basically indistinguishable from perturbative QCD at high momenta (Q >
1 GeV), and at low momenta it respects the basic analyticity properties of
spacelike observables as dictated by the general principles of the local
quantum field theories.
