Corrigendum to “QCD parameters and SM-high precision from e+e−→ Hadrons: Updated” [Nucl. Phys. A 1046 (2024) 122873]

Parts 3 and 4 of the original Abstract have been modified as:

3. I use these new values of the $D=6,8$ power corrections to extract ${\alpha }_s$ from the BNP lowest moment. To order ${\alpha }_s^4$, I find within the SVZ expansion: ${\alpha }_s\left(M_{\tau }\right){|}_{e^{+}{e}^{-}}^{SVZ}=0.3081{\left(49\right)}_{fit}{\left(71\right)}_{{\alpha }_s^5}$ [resp. $0.3260{\left(47\right)}_{fit}{\left(62\right)}_{{\alpha }_s^5}]$ implying ${\alpha }_s\left(M_Z\right){|}_{e^{+}{e}^{-}}^{SVZ}=0.1170\left(6\right){\left(3\right)}_{evol}$ [resp. $0.1192\left(6\right){\left(3\right)}_{evol}$] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: ${\alpha }_s\left(M_{\tau }\right){|}_{e^{+}{e}^{-}}^{SVZ}=0.3179{\left(58\right)}_{fit}{\left(81\right)}_{syst}$ and ${\alpha }_s\left(M_Z\right){|}_{e^{+}{e}^{-}}^{SVZ}=0.1182\left(12\right){\left(3\right)}_{evol}$ where the systematic error(syst) takes into account the discrepancy between the FO and CI results. Using the lowest BNP moment, we obtain from the vector (V) component of τ-decay data: ${\alpha }_s\left(M_{\tau }\right){|}_{\tau ,V}^{SVZ}=0.3128{\left(19\right)}_{fit}{\left(77\right)}_{{\alpha }_s^5}$ [resp. $0.3291{\left(25\right)}_{fit}{\left(65\right)}_{{\alpha }_s^5}]$ implying ${\alpha }_s\left(M_Z\right){|}_{\tau ,V}^{SVZ}=0.1176\left(10\right){\left(3\right)}_{evol}$ [resp. $0.1196\left(8\right){\left(3\right)}_{evol}$] for FO [resp. CI] PT series, giving the mean: ${\alpha }_s\left(M_{\tau }\right){|}_{\tau ,V}^{SVZ}=0.3219\left(52\right){\left(91\right)}_{syst}$ leading to: ${\alpha }_s\left(M_Z\right){|}_{\tau ,V}^{SVZ}=0.1187\left(13\right){\left(3\right)}_{evol}$. The average of the two determinations from $e^{+}{e}^{-}$ and τ-decay data is: $〈{\alpha }_s\left(M_{\tau }\right)〉=0.3198\left(72\right)$ which implies $〈{\alpha }_s\left(M_Z\right)〉=0.1185\left(9\right){\left(3\right)}_{evol}$.

4. Some (eventual) contributions beyond the SVZ expansion ($1/Q^2$, instantons and duality violation) are discussed in Sections 10 and 11 which are expected to be relatively small.