Novel Sets of Coupling Expansion Parameters for low-energy pQCD

Abstract

In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant $\al .$ However, it is known that these amplitudes are not regular functions at $α=0 .$ For QCD, we propose new sets of expansion parameters ${\bf w}_k(\as)$ that reflect singularity at $\as=0 $ and should be used instead of powers $\as^k.$ Their explicit form is motivated by the so called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level $\as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 .$ They can be used for quanitative analysis of divers low-energy amplitudes. We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.