Novel sets of coupling expansion parameters for lowenergy pQCD
Abstract
In quantum theory, physical amplitudes are usually presented in the form of a Feynman perturbation series in powers of coupling constant α. However, it is known that these amplitudes are not regular functions at α = 0. For QCD, we propose new sets of expansion parameters w _{ k }( α _{ s }) that reflect singularity at α _{ s } = 0 and should be used instead of powers α {_{/s } ^{ k }}. Their explicit form is motivated by the socalled Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level α {_{/s } ^{eff}} ( α _{ s }[Figure not available: see fulltext.] 1) = w _{1}( α _{ s }[Figure not available: see fulltext.] 1) ∼ 0.5. They can be used for the quantitative analysis of divers lowenergy amplitudes. We argue that this new picture with nonpower sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.
 Publication:

Physics of Particles and Nuclei Letters
 Pub Date:
 November 2008
 DOI:
 10.1134/S1547477108060010
 arXiv:
 arXiv:0804.0083
 Bibcode:
 2008PPNL....5..489S
 Keywords:

 12.38.Bx;
 High Energy Physics  Phenomenology
 EPrint:
 8 pages, 1 figure, submitted to Part. Nucl. Phys. Lett