# Renormalon-motivated evaluation of QCD observables

## TL;DR

This paper introduces a renormalon-inspired method for evaluating spacelike QCD observables, utilizing a Borel transform approach and Neubert-type distribution, applied to the Adler function and tau decay ratio.

## Contribution

It develops a novel renormalon-motivated evaluation technique for QCD observables using a dressed Borel transform and Neubert distribution, improving upon previous methods.

## Key findings

- Applied method to Adler function and tau decay ratio
- Compared with previous renormalization scale invariant methods
- Demonstrated improved evaluation accuracy

## Abstract

A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization scale independent only at the one-loop level, and a large-$\beta_0$-type renormalon motivated ansatz is made for the Borel transform of this quantity. This leads to a `dressed' Borel transform of the considered observable ${\cal D}(Q^2)$. From there, a Neubert-type distribution is obtained for the observable. The described method is then applied to the massless Adler function and the related decay ratio of the $\tau$ lepton semihadronic decays. Comparisons are then made with an evaluation method at higher truncated orders, developed in our earlier works, which is a renormalization scale invariant extension of the diagonal Pad\'e approximants.