Applying generalized Pad\'e approximants in analytic QCD models

TL;DR

This paper applies a generalized Padé approximant resummation method to analytic QCD models, demonstrating rapid convergence and scale independence, especially effective at low energies where traditional methods face issues.

Contribution

The authors extend a previously developed resummation method to analytic QCD models, showing its advantages over traditional scale-setting techniques and its effectiveness at low energies.

Findings

The method exhibits rapid convergence in analytic QCD models.

It provides scale-independent results for low-energy observables.

Effective in low-energy regimes where unphysical singularities are absent.

Abstract

A method of resummation of truncated perturbation series, related to diagonal Pad\'e approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of various scales and weight coefficients via an auxiliary construction of diagonal Pad\'e approximant. In low-energy QCD observables, some of these scales become sometimes low at high order, which prevents the method from being effective in perturbative QCD where the coupling has unphysical singularities at low spacelike momenta. There are no such problems in analytic QCD.