Coupling-constant analyticity and the renormalization group

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Abstract
It is shown that for all definitions of coupling constants any analytic continuation in the coupling parameter of the Green's functions of quantum chromodynamics is limited to a horn-shaped domain with zero opening angle. This extends a result of't Hooft's obtained for one specific choice of coupling parameter to all possible choices. For some choices of coupling parameter, it is also shown that the renormalization group itself leads to an analytic continuation in the coupling constant for the Green's functions regular in the above domain.