QCD parameters and SM-high precisions from e+e- to Hadrons
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| Format: | Preprint |
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2023
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| _version_ | 1866911783310065664 |
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| author | Narison, Stephan |
| author_facet | Narison, Stephan |
| contents | Using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor and the value of gluon condensate $<α_s G^2>$ from heavy quarkonia, we extract the value of the four-quark condensate : $ρα_s<\barψψ>^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and the dimension eight condensate: $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $α_s^4$. We show the inconsistency in using at the same time the standard SVZ value of the gluon and the vacuum saturation of the four-quark condensates. Using the previous values of the four-quark and $d_8$ condensates, we re-extract $<α_s G^2>$ from ${\cal R}_{10}$ to be: $(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ in perfect agreement with the one from heavy quarkonia. We also use the lowest $τ$-like decay moment ${\cal R}_τ^{ee}$ to extract the value of the QCD coupling $α_s(M^2_τ)$=0.3385(145)[resp. 0.3262(86)] (mean of fixed order (FO) and Contour Improved (CI) PT series) to order $α_s^4$ [resp. $α_s^5$] and the standard OPE. The corresponding value of the sum of the non-perturbative contribution is: $δ_{NP}(M_τ)=(3.74\pm 0.40)\times 10^{-2}$. Reciprocally, using $α_s(M_τ)$, $<α_s G^2>$ and $d_8$ as inputs, we test the stability of the value of the four-quark condensate obtained from the lowest $τ$-like moment. We complete our analysis by updating our previous determinations of the lowest order hadronic vacuum polarization contributions to the lepton anomalies and to $α(M^2_Z)$. We obtain in Table 2 : $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} $ and $α(M^2_Z)=(2766.3\pm 4.5)\times 10^{-5}$. This new value of $a_μ$ leads to: $Δa_μ\equiv a_μ^{exp}-a_μ^{th} = (142\pm 42_{th}\pm 41_{exp})\times 10^{-11}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14639 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | QCD parameters and SM-high precisions from e+e- to Hadrons Narison, Stephan High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor and the value of gluon condensate $<α_s G^2>$ from heavy quarkonia, we extract the value of the four-quark condensate : $ρα_s<\barψψ>^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and the dimension eight condensate: $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $α_s^4$. We show the inconsistency in using at the same time the standard SVZ value of the gluon and the vacuum saturation of the four-quark condensates. Using the previous values of the four-quark and $d_8$ condensates, we re-extract $<α_s G^2>$ from ${\cal R}_{10}$ to be: $(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ in perfect agreement with the one from heavy quarkonia. We also use the lowest $τ$-like decay moment ${\cal R}_τ^{ee}$ to extract the value of the QCD coupling $α_s(M^2_τ)$=0.3385(145)[resp. 0.3262(86)] (mean of fixed order (FO) and Contour Improved (CI) PT series) to order $α_s^4$ [resp. $α_s^5$] and the standard OPE. The corresponding value of the sum of the non-perturbative contribution is: $δ_{NP}(M_τ)=(3.74\pm 0.40)\times 10^{-2}$. Reciprocally, using $α_s(M_τ)$, $<α_s G^2>$ and $d_8$ as inputs, we test the stability of the value of the four-quark condensate obtained from the lowest $τ$-like moment. We complete our analysis by updating our previous determinations of the lowest order hadronic vacuum polarization contributions to the lepton anomalies and to $α(M^2_Z)$. We obtain in Table 2 : $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} $ and $α(M^2_Z)=(2766.3\pm 4.5)\times 10^{-5}$. This new value of $a_μ$ leads to: $Δa_μ\equiv a_μ^{exp}-a_μ^{th} = (142\pm 42_{th}\pm 41_{exp})\times 10^{-11}$. |
| title | QCD parameters and SM-high precisions from e+e- to Hadrons |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2306.14639 |