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

1. I report an update of my previous comparison of the theoretical value of the muon anomaly $a_{\mu }\equiv \frac{1}{2}{(g-2)}_{\mu }$ with the new measurement. One finds: $\Delta a_{\mu }\equiv a_{\mu }^{exp}-a_{\mu }^{th}=(143\pm {42}_{th}\pm {22}_{exp})\times {10}^{-11}$ indicating 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 Shifman-Vainshtein-Zahkarov (SVZ) expansion by combining the ratio of the SVZ Borel/Laplace sum rules (LSR) with the Braaten-Pich and the author (BNP) τ-like decay moments for the $I=1$ vector current. The results summarized in Table 1 confirm a violation of the factorization of the four-quark condensates and the value of the gluon one $〈{\alpha }_s{G}^2〉$ from some other sources. Up to $D=20$, I do not observe any factorial nor exponential growth of the size of these power corrections.

3. I use these new values of power corrections to extract ${\alpha }_s$ from the BNP lowest moment. To order ${\alpha }_s^4$, I find within the SVZ expansion: ${\alpha }_s\left(M_{\tau }\right)=0.3081{\left(50\right)}_{fit}{\left(71\right)}_{{\alpha }_s^5}$ [resp. $0.3260{\left(47\right)}_{fit}{\left(62\right)}_{{\alpha }_s^5}]$ implying ${\alpha }_s\left(M_Z\right)=0.1170\left(6\right){\left(3\right)}_{evol}$ [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: ${\alpha }_s\left(M_{\tau }\right){|}_{SVZ}=0.3180{\left(58\right)}_{fit}{\left(99\right)}_{syst}$ and ${\alpha }_s\left(M_Z\right){|}_{SVZ}=0.1182\left(14\right){\left(3\right)}_{evol}$ where the systematic error(syst) takes into account the discrepancy between the FO and CI results. Using the lowest BNP moment, we also obtain from the $V+A$ component of τ-decay data: ${\alpha }_s\left(M_{\tau }\right){|}_{\tau ,V+A}=0.3040{\left(76\right)}_{fit}{\left(68\right)}_{syst}$ giving: ${\alpha }_s\left(M_Z\right){|}_{\tau ,V+A}=0.1166\left(8\right){\left(3\right)}_{evol}$. The average of the two determinations from $e^{+}{e}^{-}$ and τ-decay is: $〈{\alpha }_s\left(M_{\tau }\right)〉=0.3111\left(71\right)$ which implies $〈{\alpha }_s\left(M_Z\right)〉=0.1174\left(10\right){\left(3\right)}_{evol}$.

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