Related papers: Pade Approximants and Borel Summation for QCD Pert…
In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resumming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared…
We prove that Pade approximants yield increasingly accurate predictions of higher-order coefficients in QCD perturbation series whose high-order behaviour is governed by a renormalon. We also prove that this convergence is accelerated if…
We study the renormalization-scheme (RS) dependence of Pade Approximants (PA's), and compare them with the Principle of Minimal Sensitivity (PMS) and the Effective Charge (ECH) approaches. Although the formulae provided by the PA, PMS and…
We show that the Pade Approximant (PA) approach for resummation of perturbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-$\beta_0$ limit, diagonal PA's generalize…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
The gradient expansion of the kinetic energy functional, when applied for atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the…
We propose a generalization of Grunberg's method of effective charges in which, starting with the effective charge for some dimensionless QCD observable dependent on the single energy scale $Q, R(Q)$, we introduce an infinite set of…
Pade-approximant methods are used to extract information about leading positive zeros or poles of QCD and SQCD beta-functions from the known terms of their perturbative series. For QCD, such methods are seen to corroborate the…
Pade approximations appear to be a powerful tool to extend the validity range of expansions around certain kinematical limits and to combine expansions of different limits to a single interpolating function. After a brief outline of the…
The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique…
We discuss the analytic continuation beyond $\mu/T \simeq 1$ in QCD at nonzero T and $\mu$ by use of the Pade' approximants. The slope of the critical line obtained in this way increases at large $\mu$ with respect to the second order…
Asymptotic Pade-approximant methods are utilized to estimate the leading-order unknown (i.e., not-yet-calculated) contributions to the perturbative expansions of two-current QCD correlation functions obtained from scalar-channel fermion and…
Previously developed Pade-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme…
The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field…
The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to…
We extend QCD sum rule analysis to moderate energy fixed angle Compton scattering. In this kinematic region there is a strong similarity to the sum rule treatment of electromagnetic form factors, although the four-point amplitude requires a…
Experimental data obtained for the polarized Bjorken sum rule (BSR) $\Gamma_1^{p-n}(Q^2)$ are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered:…
The reasonableness of the use of perturbative QCD notions in the region close to the scale of hadronization, i.e., below $\lesssim 1 \GeV$ is under study. First, the interplay between higher orders of pQCD expansion and higher twist…
In this paper, we consider the resummation of the divergent Rayleigh-Shrodinger perturbation expansion for the ground state energy of the quartic anharmonic oscillator in one dimension. We apply the Borel-Pade resummation method combined…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…