Novel Sets of Coupling Expansion Parameters for low-energy pQCD

TL;DR

This paper introduces new coupling expansion parameters for low-energy QCD that account for singularities at zero coupling, enabling better analysis of strong coupling regimes and revealing saturation effects.

Contribution

It proposes novel non-power expansion parameters for QCD that incorporate singularity behavior at zero coupling, extending the analytic perturbation theory framework.

Findings

Parameters reflect singularity at zero coupling

Reveal saturation at strong coupling (~0.5)

Applicable for low-energy amplitude analysis

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.