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

Abstract

1. I update my previous comparison of the theoretical value of the muon anomaly with the new measurement and found $\Delta a_{\mu }\equiv a_{\mu }^{exp}-a_{\mu }^{th}=(143\pm 42_{th}\pm 22_{exp})\times 10^{-11}$ which is about 3$\sigma$ 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 $\tau$-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 $<{\alpha }_s{G}^2>$ 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 ${\alpha }_s$ from the BNP lowest moment. To order ${\alpha }_s^4$, I find within the SVZ expansion: ${\alpha }_s(M_{\tau })=0.3081(50{)}_{fit}(71{)}_{{\alpha }_s^5}$ [resp. $0.3260(47{)}_{fit}(62{)}_{{\alpha }_s^5}]$ implying ${\alpha }_s(M_Z)=0.1170(6)(3{)}_{evol}$ [resp. $0.1192(6)(3{)}_{evol}$] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: ${\alpha }_s(M_{\tau }){|}_{SVZ}=0.3179(58{)}_{fit}(81{)}_{syst}$ and ${\alpha }_s(M_Z){|}_{SVZ}=0.1182(12)(3{)}_{evol}$ 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 $\tau$-decay the mean: ${\alpha }_s(M_{\tau }){|}_{\tau ,V}=0.3219(52)(91{)}_{syst}$ giving: ${\alpha }_s(M_Z){|}_{\tau ,V}=0.1187(13)(3{)}_{evol}$. The average of the two determinations leads to: ${\alpha }_s(M_{\tau })=0.3198(72)$ and ${\alpha }_s(M_Z)=0.1185(9)(3{)}_{evol}$. 4. Some contributions beyond the SVZ expansion ($1/Q^2$, instantons and duality violation) expected to be small are discussed in Sections 10,11.

Latex sources, 19 pages, 8 figures, 3 tables. Some preliminaries results have been presented at the alphas2024 workshop (5-9th february 2024-ECT*-Trento-IT). Section 9 on the determination of alpha_s from tau-decay has been corrected. Version published in Nucl. Phys. A + Corrigendum (to appear in Nucl. Phys. A)

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Cited by in corpus (1)

• QCD condensates and ${\alpha }_s$ from $\tau$-decay