Related papers: Asymptotic Pad\'e Approximants and the SQCD $\beta…
Perturbative QCD corrections to hadronic $\tau$ decays and $e^+e^-$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong…
One of the most troublesome contributions to the NNLO QCD corrections to B -> X_s gamma originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function…
We present the full expressions for the QCD beta-function in the MOMggg, MOMq and MOMh renormalization schemes at three loops for an arbitrary colour group in the Landau gauge. The results for all three schemes are in very good agreement…
The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Pad\'e polynomials over the Pad\'e approximation procedure. The first part of the paper is devoted to…
The successive perturbative estimates of the pressure of QCD at high temperature T show no sign of convergence, unless the coupling constant g is unrealistically small. Exploiting known results of an effective field theory which separates…
We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation.…
We prove that in the limit where the beta function is dominated by the 1-loop contribution (``large beta_0 limit'') diagonal Pad\'e Approximants (PA's) of perturbative series become exactly renormalization scale (RS) independent. This…
We determine the three-loop coefficient of the beta function in the asymmetric momentum subtraction scheme in Landau gauge. This scheme is convenient for lattice studies of \alpha_s, the running coupling constant of QCD. We present high…
The analytical method of QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric gau\-g\-e theories.…
Using high-statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we construct estimators for the radius of convergence from an eighth order series expansion of the pressure as well as the number density. We…
In the present paper, we consider $(p,q)$-analogue of the Baskakov-Beta operators and using it, we estimate some direct results on approximation. Also, we represent the convergence of these operators graphically using MATLAB.
In this paper, we estimate the simultaneous approximation exponents of the values of certain Mahler functions. For this we construct Hermite-Pad\'{e} approximations of the functions under consideration, then apply the functional equations…
We present a new estimate of the fine structure constant and the $\beta$-function of QED at an arbitrary scale. Using the non-perturbative but convergent series expression of the one loop effective action of QED that has been available…
The recent calculation of the four-loop beta function in QCD provides further evidence that the Banks-Zaks expansion in 16half-n_f is sufficiently well behaved to be useful even for n_f=2 light flavours. This expansion inherently predicts…
We study the convergence of sequences of type I and type II Hermite-Pad\'e approximants for certain systems of meromorphic functions made up of rational modifications of Nikishin systems of functions.
We discuss the long-distance physics of 2d adjoint QCD when it is viewed as an effective field theory, and determine the beta functions for its two classically-marginal four-fermi operators. These four-fermion terms preserve the invertible…
Recently E.Verlinde and H.Verlinde have suggested an effective two-dimensional theory describing the high-energy scattering in QCD. In this report we attempt to clarify some issues of this suggestion. We consider {\it anisotropic…
We calculate the three loop gauge $\beta$-function for an abelian $N=1$ supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ $\beta$-function,…
The recent determination of the $\beta$--function of the QCD running coupling $\alpha_{\overline{MS}}(Q^2)$ to 5-loops{\color{blue},} provides a verification of the convergence of a novel method for determining the fundamental QCD parameter…
Previous works show convergence of rational Chebyshev approximants to the Pad\'e approximant as the underlying domain of approximation shrinks to the origin. In the present work, the asymptotic error and interpolation properties of rational…