Perturbative expansions in QCD and analytic properties of α s

Abstract

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties,and contain in particular IR generated ghost poles and cuts. As an outcome the rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In a limiting case of large Nc, when QCD amplitudes contain only pole singularities, the strong coupling constant alpha_s(Q) is shown to be also meromorfic function of external momenta. Some simple models and examples are given when nonperturbative beta function and alpha_s(Q) can be written explicitly. General form of amplitudes at large Nc is given in the framework of background perturbation theory and its correspondence with standard perturbation theory at large momenta is demonstrated in the example of e^+e^- annihilation. For time-like momenta the background coupling constant differs drastically from the standard one but the background series averaged over energy intervals has the same (AF) asymptotics at large momenta as in the standard perturbation theory.