/ Phenomenology-HEP hep-ph/0611229


Ten years of the Analytic Perturbation Theory in QCD


Shirkov, D.V. (Dubna, JINR) ; Solovtsov, I.L. (Gomel State Tech. U.)

Published in: Theor.Math.Phys.
Year: 2007
Vol.: 150
Page No: 132-152
Pages: 26

Abstract: The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the Kallen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.

Keyword(s): nonanalyticity in alpha ; causality ; Kaellen-Lehmann representation

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