Resummation Approach in QCD Analytic Perturbation Theory

Details Resummation Approach in QCD Analytic Perturbation Theory Resummation Approach in QCD Analytic Perturbation Theory

2011-08-31

arxiv.org/abs/1108.6300v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, 2 Figures, 3 Tables. Talk presented by the first author at the International HADRON STRUCTURE'11 Conference, Tatransk

Scientific paper

10.1016/j.nuclphysbps.2011.10.09

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 $g\,\phi^4$ 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$^2$.

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