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 $\text{al}.$ However, it is known that these amplitudes are not regular functions at $\alpha =0.$ For QCD, we propose new sets of expansion parameters ${\mathbf{w}}_k(\text{as})$ that reflect singularity at $\text{as}=0$ and should be used instead of powers ${\text{as}}^k.$ Their explicit form is motivated by the so called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level ${\text{as}}^{eff}(\text{as}\gg 1)={\mathbf{w}}_1(\text{as}\gg 1)\sim \mathrm{0.5.}$ 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.

Comments: 8 pages, 1 figure, submitted to Part. Nucl. Phys. Lett