Speaker
Description
Pinched Borel-Laplace sum rules are applied to ALEPH $\tau$-decay data. For the leading-twist ($D=0$) Adler function a renormalon-motivated extension is used, whose coefficient at $(\alpha_s/\pi)^5$ is taken according to the estimate $d_4=275 \pm 63$. Two terms of dimension $D=6$ are included in the truncated OPE ($D \leq 6$), in order to enable cancellation of the corresponding renormalon ambiguities. The effective leading-order anomalous dimensions of the $D=6$ OPE operators have noninteger values (beyond large-$\beta_0$). Two variants of the fixed order perturbation theory, and the inverse Borel transform, are applied to the evaluation of the $D=0$ contribution. Truncation index $N_t$ is fixed by the requirement of local insensitivity of the momenta $a^{(2,0)}$ and $a^{(2,1)}$ under variation of $N_t$. The averaged value of the coupling obtained is $\alpha_s(m_{\tau}^2)=0.3179^{+0.0051}_{-0.0088}$ [$\alpha_s(M_Z^2)=0.1184^{+0.0007}_{-0.0011}$]. The theoretical uncertainties are significantly larger than the experimental ones.
