Resummation Approach in QCD Analytic Perturbation Theory

Abstract

We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start with a simple example of asymptotic power series for a zero-dimensional analog of the scalar $g{\varphi }^4$ model. Then we give a short historic preamble of APT and show that renormgroup improvement of the QCD perturbation theory dictates to use the Fractional APT (FAPT). After that we discuss the (F)APT resummation of nonpower series and provide the one-, two-, and three-loop resummation recipes. We show the results of applications of these recipes to the estimation of the Adler function $D(Q^2)$ in the $N_f=4$ region of $Q^2$ and of the Higgs-boson-decay width ${\Gamma }_{H\to b\bar{b}}(m_H^2)$ for $M_H=100-180$ GeV${}^2$.

8 pages, 2 Figures, 3 Tables. Talk presented by the first author at the International HADRON STRUCTURE'11 Conference, Tatranska Strba (Slovakia), June 27--July 1, 2011 and also at the International Conference "NEW TRENDS IN HIGH-ENERGY PHYSICS (experiment, phenomenology, theory)", Alushta, Crimea, Ukraine, September 3--10, 2011

References in corpus (5)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Ten years of the Analytic Perturbation Theory in QCD
• Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
• Analyticity properties of three-point functions in QCD beyond leading order

Cited by in corpus (3)

• Analogs of noninteger powers in general analytic QCD
• Operator Product Expansion with analytic QCD in tau decay physics
• Gluon Propagator in Fractional Analytic Perturbation Theory