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 $\alpha=0 .$ 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.Comment: 8 pages, 1 figure, submitted to Part. Nucl. Phys. Let