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 $\sim ({\Lambda }^2/Q^2{)}^k$ for large momenta, introducing thus nonperturbative terms $\sim ({\Lambda }^2/Q^2{)}^k$ in spacelike physical quantities whose origin is the UV regime. Consequently, it contradicts the ITEP operator product expansion 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 aforementioned ITEP 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.

• Received 21 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.114004