Novel Sets of Coupling Expansion Parameters for low-energy pQCD
arXiv:0804.0083 · doi:10.1134/S1547477108060010
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 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.
8 pages, 1 figure, submitted to Part. Nucl. Phys. Lett
References in corpus (10)
- Analytic Perturbation Theory in analyzing some QCD observables
- Ten years of the Analytic Perturbation Theory in QCD
- Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence
- Bogoliubov Renormalization Group and Symmetry of Solution in Mathematical Physics
- Group analysis and renormgroup symmetries
- Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping
- Analytic continuation and perturbative expansions in QCD
- Analytic Perturbation Theory for Practitioners and Upsilon Decay
- QCD Effective Couplings in Minkowskian and Euclidean Domains
- Analytic perturbation theory versus 1/N expansion in the Gross-Neveu model