QCD condensates and $\alpha_s$ from $\tau$-decay: Summary

TL;DR

This paper summarizes recent determinations of QCD condensates and the strong coupling constant x_s from x-decay data using Laplace sum rules and moments, highlighting the stability and consistency of the results.

Contribution

It provides a refined analysis of QCD condensates and x_s using x-decay data, addressing factorization violation and duality considerations.

Findings

Factorization of four-quark condensate is violated by a factor of 6.

No exponential growth of higher dimension condensates observed.

The extracted x_s agrees with e+e- data but may be overestimated at x-decay energies.

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) ${\cal R}_{10}^A(\tau)$ and $\tau$-like moments ${\cal R}_{n,A},\, {\cal R}_{n,V-A}$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.