Expansions of $\tau$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

TL;DR

This paper explores a novel nonpower perturbation theory framework for QCD spectral function moments, demonstrating improved convergence and reliability over standard methods, with implications for precise determination of the strong coupling from tau decays.

Contribution

It introduces a nonpower perturbation theory approach using conformal mappings that enhances convergence and renormalization-group summation for QCD spectral moments.

Findings

Nonpower perturbation theories show excellent convergence for various moments.

The new approach outperforms standard expansions in describing the Adler function.

Results support the dominance of specific renormalons in the Adler function.

Abstract

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling $\alpha_s$ and other QCD parameters from the hadronic decays of the $\tau$ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called "reference model", including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.