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

TL;DR

This paper extracts the strong coupling constant _s from tau decay data using advanced Borel-Laplace sum rules, incorporating renormalon effects and multiple perturbation methods, resulting in a precise _s value with dominant theoretical uncertainties.

Contribution

It introduces a renormalon-motivated extension for the Adler function and compares multiple perturbation approaches in sum rule analysis for _s extraction.

Findings

_s(m_ au^2)=0.3235^{+0.0138}_{-0.0126}

Theoretical uncertainties exceed experimental errors

Consistent _s values obtained across methods

Abstract

Double-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, and the 5-loop coefficient is taken to be $d_4=275 \pm 63$. Two $D=6$ terms appear in the truncated OPE ($D \leq 6$) 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 $N_t$ 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 $\alpha_s(m_{\tau}^2)=0.3235^{+0.0138}_{-0.0126}$ [$\alpha_s(M_Z^2)=0.1191 \pm 0.0016$]. The theoretical uncertainties are significantly larger than the experimental ones.