Perturbative expansions in QCD and analytic properties of α s

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Abstract
It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties and contain, in particular, infrared-generated Landau ghost poles and cuts. As an outcome, a rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In the limiting case of large Nc, where QCD amplitudes contain only pole singularities, the strong coupling constant αs(Q2) is shown to be a meromorphic function of external momenta as well. Some simple models and examples are given where nonperturbative β function and αs(Q2) can be written explicitly. The general form of amplitudes at large Nc is given in the framework of background perturbation theory, and its correspondence with standard perturbation theory at highmomenta is demonstrated in the example of e+e− annihilation. For timelike momenta, the background coupling constant differs drastically from the standard one, but the background series averaged over energy intervals has the same (AF) behavior at high momenta in the Euclidean and in the Minkowskian region.
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