Renormalon-motivated evaluation of QCD observables

A method of evaluation of spacelike QCD observables $\mathcal{D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity $\tilde{\mathcal{D}}(Q^2)$ 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 $\mathcal{D}(Q^2)$. 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.