Resummation Approach in QCD Analytic Perturbation Theory

TL;DR

This paper explores the resummation techniques in QCD Analytic Perturbation Theory, demonstrating their application to important quantities like the Adler function and Higgs decay width, improving theoretical predictions.

Contribution

It introduces resummation recipes within Fractional APT for nonpower series in QCD, extending the theoretical framework and providing practical estimation methods.

Findings

Resummation recipes for one-, two-, and three-loop calculations.

Application of these methods to the Adler function in the $N_f=4$ region.

Estimation of Higgs decay width for $M_H=100-180$ GeV.

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