Using improved operator product expansion in Borel–Laplace sum rules with ALEPH $$\tau $$ decay data, and determination of pQCD coupling

We use improved truncated Operator Product Expansion (OPE) for the Adler function, involving two types of terms with dimension $D=6$, in double-pinched Borel-Laplace Sum Rules and Finite Energy V+A channel strangeless semihadronic $\tau$ decays. The generation higher order perturbative QCD $D=0$ part function is carried out using a renormalon-motivated ansatz incorporating leading UV renormalon first IR renormalons. trunacted evaluated by variants fixed-order perturbation theory (FO), Principal Value Borel resummation (PV), contour-improved (CI). For experimental spectral we ALEPH $\tau$-decay data. point that FO PV evaluation methods account correctly structure Rules, while this not case CI evaluation. extract value ${\overline {\rm MS}}$ coupling $\alpha_s(m_{\tau}^2) = 0.3235^{+0.0138}_{-0.0126}$ [$\alpha_s(M_Z^2)=0.1191 \pm 0.0016$] average method, which consider as our main result. If included also extraction, would be 0.3299^{+0.0232}_{-0.0225}$ [$\alpha_s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}$]. This work an extension improvement previous [Eur.Phys.J.C81 (2021) 10, 930] where used OPE more naive (and widely used) form extracted values $\alpha_s(M_Z^2)$ were somewhat lower.