Related papers: Thresholds in FAPT: Euclid vs Minkowski

We give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of squared momentum transfer q^2, which takes into account heavy-quark…

We work out and discuss the Minkowski version of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed and presented by us for the Euclidean region. The original analytic approach to QCD, initiated by…

We describe the generalization of Analytic Perturbation Theory (APT) for QCD observables, initiated by Radyushkin, Krasnikov, Pivovarov, Shirkov and Solovtsov, to fractional powers of coupling -- Fractional APT (FAPT). The basic aspects of…

We give a short introduction to the Analytic Perturbation Theory (APT) and its generalization to Fractional powers -- FAPT. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the…

We describe the development of Analytic Perturbation Theory (APT) in QCD, called Fractional APT (FAPT), which has been suggested to apply the renormalization group evolution and QCD factorization technique in the framework of APT.

This talk describes the resummation approach in (Fractional) Analytic Perturbation Theory (FAPT) in QCD. First, we make a short historical review of the (F)APT approach and then shortly describe the global scheme of FAPT which allows one to…

We provide here all the procedures in \texttt{Mathematica} which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (${\bar{\mathfrak A}_{\nu}(s;n_f)}$ and ${\mathfrak…

Here, we report briefly two topics: 1) The latest version of ``Analytic Perturbation Theory" (APT) devised recently for the QCD observables both in the Euclidean and Minkowskian regions. 2) Results of the APT--based calculation for some…

The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this,…

We give a short introduction to the Analytic Perturbation Theory (APT) in QCD, discuss its problems and how they can be resolved in Fractional APT (FAPT), and give a brief report about taking into account heavy-quark thresholds in FAPT.…

We present new results on the summation of nonpower-series expansions in QCD Analytic Perturbation Theory (APT) in the one-loop approximation. We show how to generalize the approach suggested by one of us earlier to the cases of APT and…

The connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions is studied. Our basic tool is the "double spectral representation", similar to definition of Adler function,…

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and…

The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\alpha$, in Quantum Theory. We start with outlining a…

Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to…

Different ``analytization'' procedures for the factorized pion form factor are discussed in comparison with the standard QCD perturbation theory at NLO. It is argued that demanding the analyticity of the exclusive amplitude as a…

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…

We consider computational problems in the framework of nonpower Analityc Perturbation Theory and Fractional Analytic Perturbation Theory that are the generalization of the standard QCD perturbation theory. The singularity-free, finite…

Different methods for treating the results of higher-order perturbative QCD calculations of the decay width of the Standard Model Higgs boson into bottom quarks are discusssed. Special attention is paid to the analysis of the $M_H$…

We discuss the application of an analytic approach called the analytic perturbation theory (APT) to the QCD analysis of DIS data. In particular, the results of the QCD analysis of a set of `fake' data on the polarized nonsinglet Delta{q3}…