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

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.Comment: 8 pages, 8 figures. Type and language correction. New references. Version to be publishe

QCD fixed points: Banks-Zaks scenario or dynamical gluon mass generation?

Fixed points in QCD can appear when the number of quark flavors ($N_f$) is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass generation (DGM) does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their $\beta$ functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large $N_f$, we verify that near the so called QCD conformal window both cases exhibit fixed points at similar coupling constant values ($g^*$). We argue that the states of minimum vacuum energy, as a function of the coupling constant up to $g^*$ and for several $N_f$ values, are related to the dynamical gluon mass generation mechanism.Comment: 9 pages, 9 figures, new references, improved discussion and small change in the title, to appear in IJMP