QCD parameters and SM-high precisions from e+e−→ Hadrons

Using the PDG 22 compilation of e+e−→ Hadrons ⊕ recent CMD3 data for pion form factor and value gluon condensate 〈αsG2〉 from heavy quarkonia, we extract four-quark condensate: ραs〈ψ¯ψ〉2=(5.98±0.64)×10−4 GeV6 dimension eight d8=(4.3±3.0)×10−2 GeV8 ratio R10 Laplace sum rules to order αs4. We show inconsistency in using at same time standard SVZ vacuum saturation condensates. previous values d8 condensates, re-extract be: (6.12±0.61)×10−2 Gev4 perfect agreement with one quarkonia. also use lowest τ-like decay moment Rτee QCD coupling. obtain O(αs4) mean FO (fixed order) CI (contour improved) PT series within OPE: αs(Mτ)=0.3385(50)(136)syst where last error is an added conservative systematic distance central values. Assuming that αs-coefficients grow geometrically as observed calculated case, O(αs5): αs(Mτ)=0.3262(37)(78)syst. These results lead to: αs(MZ)=0.1207(17)(3) [resp. 0.1193(11)(3)] αs4 αs5]. The corresponding non-perturbative contribution Mτ is: δNPV(Mτ)=(2.3±0.2)×10−2. Reciprocally, αs(Mτ), inputs, test stability obtained moment. complete our analysis by updating determinations hadronic polarization contributions lepton anomalies α(MZ2). Table 3: aμ|l.ohvp=(7036.5±38.9)×10−11,aτ|l.ohvp=(3494.8±24.7)×10−9. α(5)(MZ)|had=(2766.3±4.5)×10−5. This new aμ leads Δaμ≡aμexp−aμth=(142±42th±41exp)×10−11. which reduces tension between SM prediction experiment.