QCD parameters and SM-high precisions from $e^+e^-\to$ Hadrons : Summary
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| Natura: | Preprint |
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2023
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| _version_ | 1866914689409089536 |
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| author | Narison, Stephan |
| author_facet | Narison, Stephan |
| contents | In this talk, I summarize the results obtained recently in Ref.\,\cite{SNe} using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor. Using the gluon condensate $\langle α_s G^2\rangle=(6.49\pm 0.35)\times 10^{-2}$ GeV$^4$ from heavy quark sum rules, the extracted QCD four-quark and dimension eight condensate condensates values are: $ρα_s\langle\barψψ\rangle^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$ from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $α_s^4$. Inversely using these estimated values of the condensates, we obtain from ${\cal R}_{10}$: $\langle α_s G^2\rangle=(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ which leads to the average $(6.40\pm 0.30)\times 10^{-2}$ GeV$^4$. %from light and heavy quark systems. Using the lowest $τ$-like decay moment, the mean result of Fixed Order (FO) and Contour Improved (CI) PT series within the standard OPE is : $α_s(M_τ)=0.3385(50)(136)_{syst}$ [resp. $0.3262(37)(78)_{syst}$] to order $α_s^4$ [resp. $α_s^5$] leading to $α_s(M_Z)$=0.1207(17)(3) [resp. 0.1193(11)(3)], while the sum of the non-perturbative contribution at $M_τ$ is\,: $δ^V_{NP}(M_τ)=(2.3\pm 0.2)\times 10^{-2}$. Using the same data, one also obtains the LO hadronic vacuum polarization to the muon and $τ$ anomalous magnetic moments: $a_μ\vert^{hvp}_{l.o}= (7036.5\pm 38.9)\times10^{-11}, \, a_τ\vert^{hvp}_{l.o}= (3494.8\pm 24.7)\times10^{-9} $ which leads to : $Δa_μ\equiv a_μ^{exp}-a_μ^{th} = (143\pm 42_{th}\pm 22_{exp})\times 10^{-11}$ indicating about 3$σ$ discrepancy between the SM predictions and experiment. One also finds: $α^{(5)}(M_Z)\vert_{had}=(2766.3\pm 4.5)\times 10^{-5}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05342 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | QCD parameters and SM-high precisions from $e^+e^-\to$ Hadrons : Summary Narison, Stephan High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice In this talk, I summarize the results obtained recently in Ref.\,\cite{SNe} using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor. Using the gluon condensate $\langle α_s G^2\rangle=(6.49\pm 0.35)\times 10^{-2}$ GeV$^4$ from heavy quark sum rules, the extracted QCD four-quark and dimension eight condensate condensates values are: $ρα_s\langle\barψψ\rangle^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$ from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $α_s^4$. Inversely using these estimated values of the condensates, we obtain from ${\cal R}_{10}$: $\langle α_s G^2\rangle=(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ which leads to the average $(6.40\pm 0.30)\times 10^{-2}$ GeV$^4$. %from light and heavy quark systems. Using the lowest $τ$-like decay moment, the mean result of Fixed Order (FO) and Contour Improved (CI) PT series within the standard OPE is : $α_s(M_τ)=0.3385(50)(136)_{syst}$ [resp. $0.3262(37)(78)_{syst}$] to order $α_s^4$ [resp. $α_s^5$] leading to $α_s(M_Z)$=0.1207(17)(3) [resp. 0.1193(11)(3)], while the sum of the non-perturbative contribution at $M_τ$ is\,: $δ^V_{NP}(M_τ)=(2.3\pm 0.2)\times 10^{-2}$. Using the same data, one also obtains the LO hadronic vacuum polarization to the muon and $τ$ anomalous magnetic moments: $a_μ\vert^{hvp}_{l.o}= (7036.5\pm 38.9)\times10^{-11}, \, a_τ\vert^{hvp}_{l.o}= (3494.8\pm 24.7)\times10^{-9} $ which leads to : $Δa_μ\equiv a_μ^{exp}-a_μ^{th} = (143\pm 42_{th}\pm 22_{exp})\times 10^{-11}$ indicating about 3$σ$ discrepancy between the SM predictions and experiment. One also finds: $α^{(5)}(M_Z)\vert_{had}=(2766.3\pm 4.5)\times 10^{-5}$. |
| title | QCD parameters and SM-high precisions from $e^+e^-\to$ Hadrons : Summary |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2309.05342 |