QCD parameters and SM-high precisions from $e^{+}{e}^{-}\to$ Hadrons : Summary

In this talk, I summarize the results obtained recently in Ref.,\cite{SNe} using the PDG 22 compilation of the $e^{+}{e}^{-}\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor. Using the gluon condensate $⟨{\alpha }_s{G}^2⟩=(6.49\pm 0.35)\times {10}^{-2}$ GeV${}^4$ from heavy quark sum rules, the extracted QCD four-quark and dimension eight condensate condensates values are: $\rho {\alpha }_s⟨\bar{\psi }\psi {⟩}^2=(5.98\pm 0.64)\times {10}^{-4}$ GeV${}^6$ and $d_8=(4.3\pm 3.0)\times {10}^{-2}$ GeV${}^8$ from the ratio ${\mathcal{R}}_{10}$ of Laplace sum rules to order ${\alpha }_s^4$. Inversely using these estimated values of the condensates, we obtain from ${\mathcal{R}}_{10}$: $⟨{\alpha }_s{G}^2⟩=(6.12\pm 0.61)\times {10}^{-2}$ GeV${}^4$ which leads to the average $(6.40\pm 0.30)\times {10}^{-2}$ GeV${}^4$. %from light and heavy quark systems. Using the lowest $\tau$-like decay moment, the mean result of Fixed Order (FO) and Contour Improved (CI) PT series within the standard OPE is : ${\alpha }_s(M_{\tau })=0.3385(50)(136{)}_{syst}$ [resp. $0.3262(37)(78{)}_{syst}$] to order ${\alpha }_s^4$ [resp. ${\alpha }_s^5$] leading to ${\alpha }_s(M_Z)$=0.1207(17)(3) [resp. 0.1193(11)(3)], while the sum of the non-perturbative contribution at $M_{\tau }$ is,: ${\delta }_{NP}^V(M_{\tau })=(2.3\pm 0.2)\times {10}^{-2}$. Using the same data, one also obtains the LO hadronic vacuum polarization to the muon and $\tau$ anomalous magnetic moments: $a_{\mu }{\mathrm{\mid }}_{l\mathrm{.}o}^{hvp}=(7036.5\pm 38.9)\times {10}^{-11},a_{\tau }{\mathrm{\mid }}_{l\mathrm{.}o}^{hvp}=(3494.8\pm 24.7)\times {10}^{-9}$ which leads to : $\mathrm{\Delta }{a}_{\mu }\equiv a_{\mu }^{exp}-a_{\mu }^{th}=(143\pm {42}_{th}\pm {22}_{exp})\times {10}^{-11}$ indicating about 3$\sigma$ discrepancy between the SM predictions and experiment. One also finds: ${\alpha }^{(5)}(M_Z){\mathrm{\mid }}_{had}=(2766.3\pm 4.5)\times {10}^{-5}$.