QCD parameters and SM-high precisions from $e^+e^-\to$ Hadrons : Summary

TL;DR

This paper summarizes recent results on QCD parameters and Standard Model precision tests derived from $e^+e^- o$ Hadrons data, including condensate values, strong coupling constants, and muon magnetic moment contributions, highlighting a 3-sigma discrepancy with experiments.

Contribution

It provides updated determinations of QCD condensates, strong coupling constants, and hadronic contributions to magnetic moments using recent experimental data and sum rule analyses.

Findings

Estimated gluon condensate value: (6.40 ± 0.30)×10^{-2} GeV^4

Strong coupling at M_Z: 0.1193–0.1207 with uncertainties

Muon g-2 discrepancy: about 3σ between SM prediction and experiment

Abstract

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 $\langle \alpha_s G^2\rangle=(6.49\pm 0.35)\times 10^{-2}$ GeV$^4$ from heavy quark sum rules, the extracted QCD four-quark and dimension eight condensate condensates values are: $\rho\alpha_s\langle\bar\psi\psi\rangle^2= (5.98\pm 0.64)\times 10^{-4}$ 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 $\alpha_s^4$. Inversely using these estimated values of the condensates, we obtain from ${\cal R}_{10}$: $\langle \alpha_s G^2\rangle=(6.12\pm 0.61)\times 10^{-2}$ 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 $\tau$-like decay moment, the mean result of Fixed Order (FO) and Contour Improved (CI) PT series within the standard OPE is : $\alpha_s(M_\tau)=0.3385(50)(136)_{syst}$ [resp. $0.3262(37)(78)_{syst}$] to order $\alpha_s^4$ [resp. $\alpha_s^5$] leading to $\alpha_s(M_Z)$=0.1207(17)(3) [resp. 0.1193(11)(3)], while the sum of the non-perturbative contribution at $M_\tau$ is\,: $\delta^V_{NP}(M_\tau)=(2.3\pm 0.2)\times 10^{-2}$. Using the same data, one also obtains the LO hadronic vacuum polarization to the muon and $\tau$ anomalous magnetic moments: $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} $ which leads to : $\Delta a_\mu\equiv a_\mu^{exp}-a_\mu^{th} = (143\pm 42_{th}\pm 22_{exp})\times 10^{-11}$ indicating about 3$\sigma$ discrepancy between the SM predictions and experiment. One also finds: $\alpha^{(5)}(M_Z)\vert_{had}=(2766.3\pm 4.5)\times 10^{-5}$.