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

Abstract

In this talk, I summarize the results obtained recently in Ref. [1] using the PDG 22 compilation of the e+e−→ Hadrons ⊕ the recent CMD3 data for the pion form factor. Using the gluon condensate 〈αsG2〉=(6.49±0.35)×10−2 GeV4 from heavy quark sum rules, the extracted QCD four-quark and dimension eight condensate condensates values are: ραs〈ψ¯ψ〉2=(5.98±0.64)×10−4 GeV6 and d8=(4.3±3.0)×10−2 GeV8 from the ratio R10 of Laplace sum rules to order αs4. Inversely using these estimated values of the condensates, we obtain from R10: 〈αsG2〉=(6.12±0.61)×10−2 GeV4 which leads to the average (6.40±0.30)×10−2 GeV4. Using the lowest τ-like decay moment, the mean result of Fixed Order (FO) and Contour Improved (CI) PT series within the standard OPE is: αs(Mτ)=0.3385(50)(136)syst [resp. 0.3262(37)(78)syst] to order αs4 [resp. αs5] leading to αs(MZ)=0.1207(17)(3) [resp. 0.1193(11)(3)], while the sum of the non-perturbative contribution at Mτ is: δNPV(Mτ)=(2.3±0.2)×10−2. Using the same data, one also obtains the LO hadronic vacuum polarization to the muon and τ anomalous magnetic moments: aμ|l.ohvp=(7036.5±38.9)×10−11,aτ|l.ohvp=(3494.8±24.7)×10−9 which leads to: Δaμ≡aμexp−aμth=(143±42th±22exp)×10−11 indicating about 3σ discrepancy between the SM predictions and experiment. One also finds: α(5)(MZ)|had=(2766.3±4.5)×10−5.