Asymptotic structure of perturbative series for tau lepton observables

TL;DR

This paper investigates the asymptotic behavior of perturbative series in tau lepton decay observables, identifying the order at which divergence begins and assessing the precision of finite order predictions.

Contribution

It provides a scheme-invariant analysis of the onset of asymptotic growth in perturbation series for tau decay, and discusses optimal observable construction.

Findings

Asymptotic growth starts at  order in perturbation series.

Finite order predictions have a quantifiable ultimate accuracy.

Optimal observables can be constructed for improved analysis.

Abstract

We analyze tau lepton decay observables, namely moments of the hadronic spectral density in the finite energy interval (0,M_\tau), within finite order perturbation theory including \alpha_s^4 corrections. The start of asymptotic growth of perturbation theory series is found at this order in a scheme invariant manner. We establish the ultimate accuracy of finite order perturbation theory predictions and discuss the construction of optimal observables.