Related papers: Resummation in (F)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 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 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 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) 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.…
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…
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…
We give a short introduction to the Analytic Perturbation Theory (APT) in QCD, describe its problems and suggest as a tool for their resolution the Fractional APT (FAPT). We also describe shortly how to treat heavy-quark thresholds in FAPT.…
We propose to resum exactly any number of one-loop vacuum polarization insertions into the scale of the coupling of lowest order radiative corrections. This makes maximal use of the information contained in one-loop perturbative corrections…
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…
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD -- ghost singularities and…
We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED X QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and…
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…
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…
In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of…
We analyze two sets of specific functions, that/which form the basis of the nonpower asymptotic expansions both in the timelike and spacelike regions for single scale dependent QCD observables in the Shirkov--Solovtsov's Analytic…
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.
We compute the decay rate of the Standard Model Higgs boson to bottom quarks to order $\alpha\alpha_s$. We apply the optical theorem and calculate the imaginary part of three-loop corrections to the Higgs boson propagator using asymptotic…
We present the current status of the application of our approach of exact amplitude-based resummation in quantum field theory to two areas of investigation: precision QCD calculations of all three of us as needed for LHC physics and the…
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,…