$R_{e^{+}{e}^{-}}$ and an effective QCD charge

Abstract

We consider the electron-positron annihilation process into hadrons $R_{e^{+}{e}^{-}}$ up to $\mathcal{O}({\alpha }_s^3)$ and we adopt the smearing method suggest by Poggio, Quinn and Weinberg to confront the experimental data with theory. As a theoretical model we use a QCD coupling constant frozen in the low energy regime, where this coupling can be parameterised in terms of an effective dynamical gluon mass ($m_g$) which is determined through Schwinger-Dyson equations. In order to find the best fit between experimental data and theory we perform a ${\chi }^2$ study, that, within the uncertainties of the approach, has a minimum value when $m_g/{\Lambda }_{QCD}$ is in the range $1.2-1.4$. These values are in agreement with other phenomenological determinations of this ratio and lead to an infrared effective charge ${\alpha }_s(0)\approx 0.7$. We comment how this effective charge may affect the global duality mass scale that indicates the frontier between perturbative and non-perturbative physics.

Comments: 8 pages, 8 figures. Type and language correction. New references. Version to be published