QCD parameters and SM-high precision from e⁺e⁻ to Hadrons: Updated

I update my previous comparison of the theoretical value of the muon anomaly with the new measurement and found Δ a_μ≡ a_μᵉˣᵖ-a_μᵗʰ = (143± 42ₜₕ± 22ₑₓₚ)× 10⁻¹¹ which is about 3σ discrepancy between the SM predictions and experiment. 2. I improve the estimate of QCD power corrections up to dimension D=12 and provide a new estimate of the ones up to D=20 within the SVZ expansion by combining the ratio of the Laplace sum rules (LSR) with the BNP τ-like decay moments for the I=1 vector current. The results in Table 1 confirm a violation of the factorization of the four-quark condensates and the value of the gluon one <αₛ G²> from some other sources. Up to D=20, I there is not any factorial nor exponential growth of the size of these power corrections. 3. I use these new values of power corrections to extract αₛ from the BNP lowest moment. To order αₛ⁴, I find within the SVZ expansion: αₛ(M_τ)= 0.3081(50)fit(71)αₛ⁵ [resp. 0.3260 (47)fit(62)αₛ⁵] implying αₛ(MZ)= 0.1170(6)(3)ₑᵥₒₗ [resp. 0.1192(6)(3)ₑᵥₒₗ] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: αₛ(M_τ)SVZ=0.3179(58)fit(81)syst and αₛ(MZ)SVZ= 0.1182(12)(3)ₑᵥₒₗ where the systematic error(syst) takes into account the discrepancy between FO and CI. Using the lowest BNP moment, we also obtain from the vector (V) component of τ-decay the mean: αₛ(M_τ)τ,V=0.3219(52)(91)syst giving: αₛ(MZ)τ,V=0.1187(13)(3)ₑᵥₒₗ. The average of the two determinations leads to: αₛ(M_τ)=0.3198(72) and αₛ(MZ)= 0.1185(9)(3)ₑᵥₒₗ. 4. Some contributions beyond the SVZ expansion (1/Q², instantons and duality violation) expected to be small are discussed in Sections 10,11.