QCD condensates and ${\alpha }_s$ from $\tau$-decay: Summary

Abstract

In this talk, I summarize the recent determinations in Ref.[1] of the QCD condensates and ${\alpha }_s$ within the SVZ expansion using the ratio of Laplace sum rule (LSR) ${\mathcal{R}}_{10}^A(\tau )$ and $\tau$-like moments ${\mathcal{R}}_{n,A},{\mathcal{R}}_{n,V-A}$within stability criteria in the axial-vector (A) and V-A channels of the $\tau$- semi-hadronic decays. The factorization of the four-quark condensate is violated by a factor 6 like in the case of the $e^{+}{e}^{-}\to$ Hadrons data. There is no exponential growth of the size of higher dimension condensates which does not favour (by duality) a significant effect of the so-called Duality Violation (DV). The extracted value of ${\alpha }_s$ is in good agreement with the one from $e^{+}{e}^{-}$ and indicates that the determination at the observed $\tau$-mass is not the optimal one and leads to an overestimate of its actual value.

Comments: Latex sources, 15 pages, 6 figures, 3 tables, Talk given at the 14th International Conference in High-Energy Physics (HEPMAD24), 21-26th October 2024, Antananarivo, MG. Version to appear in Journal of Subatomic Particles and Cosmology. arXiv admin note: substantial text overlap with arXiv:2408.05732