English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recentCMD3 data for the pion form factor and the value of gluon condensate $<\alpha_sG^2>$ from heavy quarkonia, we extract the value of the four-quark condensate :$\rho\alpha_s<\bar\psi\psi>^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and thedimension eight condensate: $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$from theratio ${\cal R}_{10}$ of Laplace sum rules to order $\alpha_s^4$. We show theinconsistency in using at the same time the standard SVZ value of the gluon andthe vacuum saturation of the four-quark condensates. Using the previous valuesof the four-quark and $d_8$ condensates, we re-extract $<\alpha_s G^2>$ from${\cal R}_{10}$ to be: $(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ in perfectagreement with the one from heavy quarkonia. We also use the lowest $\tau$-likedecay moment ${\cal R}_\tau^{ee}$ to extract the value of the QCD coupling$\alpha_s(M^2_\tau)$=0.3385(145)[resp. 0.3262(86)] (mean of fixed order (FO)and Contour Improved (CI) PT series) to order $\alpha_s^4$ [resp. $\alpha_s^5$]and the standard OPE. The corresponding value of the sum of thenon-perturbative contribution is: $\delta_{NP}(M_\tau)=(3.74\pm 0.40)\times10^{-2}$. Reciprocally, using $\alpha_s(M_\tau)$, $<\alpha_s G^2>$ and $d_8$ asinputs, we test the stability of the value of the four-quark condensateobtained from the lowest $\tau$-like moment. We complete our analysis byupdating our previous determinations of the lowest order hadronic vacuumpolarization contributions to the lepton anomalies and to $\alpha(M^2_Z)$. Weobtain in Table 2 : $a_\mu\vert^{hvp}_{l.o}= (7036.5\pm 38.9)\times10^{-11},a_\tau\vert^{hvp}_{l.o}= (3494.8\pm 24.7)\times10^{-9} $ and$\alpha(M^2_Z)=(2766.3\pm 4.5)\times 10^{-5}$. This new value of $a_\mu$ leadsto: $\Delta a_\mu\equiv a_\mu^{exp}-a_\mu^{th} = (142\pm 42_{th}\pm41_{exp})\times 10^{-11}$.

QCD parameters and SM-high precisions from e+e- to Hadrons