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

Abstract

1. I report an update of my previous comparison of the theoretical value of the muon anomaly aμ≡12(g−2)μ with the new measurement. One finds: Δaμ≡aμexp−aμth=(143±42th±22exp)×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 〈αsG2〉 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 αs from the BNP lowest moment. To order αs4, I find within the SVZ expansion: αs(Mτ)=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(Mτ)|SVZ=0.3180(58)fit(99)syst and αs(MZ)|SVZ=0.1182(14)(3)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: αs(Mτ)|τ,V+A=0.3040(76)fit(68)syst giving: αs(MZ)|τ,V+A=0.1166(8)(3)evol. The average of the two determinations from e+e− and τ-decay is: 〈αs(Mτ)〉=0.3111(71) which implies 〈αs(MZ)〉=0.1174(10)(3)evol.4. Some (eventual) contributions beyond the SVZ expansion (1/Q2, instantons and duality violation) are discussed in Sections 10 and 11.