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 $Δ a_{μ} \equiv a_{μ}^{e x p} - a_{μ}^{t h} = (143 \pm 42_{t h} \pm 22_{e x p}) \times 10^{- 11}$ which is about 3 $σ$ 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 $< α_{s} G^{2} >$ 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 $α_{s}$ from the BNP lowest moment. To order $α_{s}^{4}$ , I find within the SVZ expansion: $α_{s} (M_{τ}) = 0.3081 (50)_{f i t} (71)_{α_{s}^{5}}$ [resp. $0.3260 (47)_{f i t} (62)_{α_{s}^{5}}]$ implying $α_{s} (M_{Z}) = 0.1170 (6) (3)_{e v o l}$ [resp. $0.1192 (6) (3)_{e v o l}$ ] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: $α_{s} (M_{τ}) ∣_{S V Z} = 0.3179 (58)_{f i t} (81)_{s y s t}$ and $α_{s} (M_{Z}) ∣_{S V Z} = 0.1182 (12) (3)_{e v o l}$ 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: $α_{s} (M_{τ}) ∣_{τ, V} = 0.3219 (52) (91)_{s y s t}$ giving: $α_{s} (M_{Z}) ∣_{τ, V} = 0.1187 (13) (3)_{e v o l}$ . The average of the two determinations leads to: $α_{s} (M_{τ}) = 0.3198 (72)$ and $α_{s} (M_{Z}) = 0.1185 (9) (3)_{e v o l}$ . 4. Some contributions beyond the SVZ expansion ( $1 / Q^{2}$ , instantons and duality violation) expected to be small are discussed in Sections 10,11.

I update my previous comparison of the theoretical value of the muon anomaly with the new measurement and found $Δ a_{μ} \equiv a_{μ}^{e x p} - a_{μ}^{t h} = (143 \pm 42_{t h} \pm 22_{e x p}) \times 10^{- 11}$ which is about 3 $σ$ 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 $< α_{s} G^{2} >$ 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 $α_{s}$ from the BNP lowest moment. To order $α_{s}^{4}$ , I find within the SVZ expansion: $α_{s} (M_{τ}) = 0.3081 (50)_{f i t} (71)_{α_{s}^{5}}$ [resp. $0.3260 (47)_{f i t} (62)_{α_{s}^{5}}]$ implying $α_{s} (M_{Z}) = 0.1170 (6) (3)_{e v o l}$ [resp. $0.1192 (6) (3)_{e v o l}$ ] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: $α_{s} (M_{τ}) ∣_{S V Z} = 0.3179 (58)_{f i t} (81)_{s y s t}$ and $α_{s} (M_{Z}) ∣_{S V Z} = 0.1182 (12) (3)_{e v o l}$ 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: $α_{s} (M_{τ}) ∣_{τ, V} = 0.3219 (52) (91)_{s y s t}$ giving: $α_{s} (M_{Z}) ∣_{τ, V} = 0.1187 (13) (3)_{e v o l}$ . The average of the two determinations leads to: $α_{s} (M_{τ}) = 0.3198 (72)$ and $α_{s} (M_{Z}) = 0.1185 (9) (3)_{e v o l}$ . 4. Some contributions beyond the SVZ expansion ( $1 / Q^{2}$ , instantons and duality violation) expected to be small are discussed in Sections 10,11.

QCD parameters and SM-high precision from $e^{+} e^{-}$ to Hadrons: Updated

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QCD parameters and SM-high precision from $e^{+} e^{-}$ to Hadrons: Updated

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

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

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QCD parameters and SM-high precision from $e^{+} e^{-}$ to Hadrons: Updated

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QCD parameters and SM-high precision from $e^{+} e^{-}$ to Hadrons: Updated

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