Determination of α_s value from tau decays with a renormalon-motivated approach

¹ Instituto de Alta Investigación, Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren 2477, Iquique, Chile
² Department of Physics, Universidad Técnica Federico Santa María (UTFSM), Avenida España 1680, Valparaíso, Chile

^* e-mail: cayalan@academicos.uta.cl
^** e-mail: gorazd.cvetic@gmail.com
^*** e-mail: diego.teca@usm.cl

Published online: 22 December 2022

Abstract

We apply Borel-Laplace sum rules to the data of the semihadronic tau decay rate. For the higher order terms of the Adler function in the leadingtwist (D = 0) contribution we use a renormalon-motivated model, where the correct leading anomalous dimensions are taken into account in the IR u = 3 (and u = 2) renormalon contributions. In the evaluation of D = 0 contribution of the sum rules we apply two methods: (a) fixed order perturbation theory (FO) and (b) Borel resummation of the singular part with the Principal Value prescription (PV). We use as data the ALEPH data for the (V+A)-channel, and a combined set of data for the V-channel. In the D = 6 OPE term of the Adler function we account for the leading nonzero (and noninteger) anomalous dimension. In the OPE for the Adler function we include terms with dimension up to D = 10 for the (V+A)-channel, and up to D = 14 for the V-channel. In such cases, the extracted values of the coupling α_s and of the condensates show a reasonably good convergence under the increase of OPE terms. In order to suppress the quark-hadron duality violations, our sum rules are doubly-pinched in the Minkowskian point. We obtain the averaged extracted values of the coupling α_s(m²_τ) = 0.3169^+0.0070_-0.0096, corresponding to α_s(M²_Z) = 0.1183^+0.0009_-0.0012.