aμ|l.ohvp, QCD power corrections and αs from e+e− → Hadrons

Abstract

In this talk, I review the results obtained recently in Ref. [1]. First, we estimate the LO hadronic vacuum polarization contribution to the muon and τ anomalous magnetic moments to be: $a_{\mu }{|}_{l.o}^{hvp}=(7036.5\pm 38.9)\times {10}^{-11}$, $a_{\tau }{|}_{l.o}^{hvp}=(3494.8\pm 24.7)\times {10}^{-9}$ (see Table 1) leading to: $\Delta a_{\mu }\equiv a_{\mu }^{exp}-a_{\mu }^{SM}=(143\pm {42}_{th}\pm {22}_{exp})\times {10}^{-11}$ which is about 3σ discrepancy between the SM predictions and experiment. One also finds: ${\alpha }^{\left(5\right)}\left(M_Z\right){|}_{had}=(2766.3\pm 4.5)\times {10}^{-5}$. Second, we estimate the QCD power corrections up to dimension 20 from the ratio of Laplace sum rule and from τ-like decay high moments (see Table 3). We do not observe any exponential growth of their size which may not favour a duality violation of the spectral function. We obtain $〈{\alpha }_s{G}^2〉=(7.8\pm 3.5)\times {10}^{-2}{\text{GeV}}^4$ in agreement with the more precise one from heavy quark sum rules, while $\rho {\alpha }_s{〈\overline{\psi }\psi 〉}^2=(5.98\pm 0.64)\times {10}^{-4}{\text{GeV}}^6$ confirms a violation of the four-quark condensate factorization by a factor $\rho \simeq 6$. Third, using the previous values of the condensates, we re-extract ${\alpha }_s$ from the lowest τ-decay Braaten-SN-Pich (BNP) moment and find to order ${\alpha }_s^4:{\alpha }_s\left(M_{\tau }\right)=0.3081\left(86\right)\left[\mathrm{resp}.0.3260\right(79\left)\right]⟶\circ {\alpha }_s\left(M_Z\right)=0.1170\left(7\right)\left[\mathrm{resp}.0.1192\right(7\left)\right]$ for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. We also show that the contributions beyond the Shifman-Vainshtein-Zakharov (SVZ)-expansion are negligible.