Extraction of $α_s$ using Borel-Laplace sum rules for tau decay data

Abstract

Double-pinched Borel-Laplace sum rules are applied to ALEPH τ -decay data. For the leadingtwist (D = 0) Adler function a renormalon-motivated extension is used, and the 5-loop coefficient is taken to be d4 = 275 ± 63. Two D = 6 terms appear in the truncated OPE (D ≤ 6) to enable cancellation of the corresponding renormalon ambiguities. 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 Nt is fixed by the requirement of local insensitivity of the momenta a (2,0) and a (2,1) under variation of Nt. The averaged value of the coupling obtained is αs(m 2 τ ) = 0.3235 +0.0138 −0.0126 [αs(M 2 Z ) = 0.1191 ± 0.0016]. The theoretical uncertainties are significantly larger than the experimental ones.