$R_{e^{+}{e}^{-}}$ 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.

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

References in corpus (18)

• The QCD transition temperature: results with physical masses in the continuum limit II.
• Equation of state and QCD transition at finite temperature
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Pinch Technique: Theory and Applications
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Infrared propagators of Yang-Mills theory from perturbation theory
• Non-perturbative comparison of QCD effective charges
• Chiral symmetry breaking with lattice propagators
• Yang-Mills two-point functions in linear covariant gauges
• Alternative refined Gribov-Zwanziger Lagrangian
• Entropy, confinement, and chiral symmetry breaking
• On the dynamical mass generation in confining Yang-Mills theories
• Non-perturbative fixed points and renormalization group improved effective potential
• QCD chiral symmetry restoration with a large number of quarks in a model with a confining propagator and dynamically massive gluons
• The gluon mass generation mechanism: a concise primer

Cited by in corpus (3)

• On the Interface between Perturbative and Nonperturbative QCD
• Anomalous mass dimension of multi-flavor QCD
• QCD fixed points: Banks-Zaks scenario or dynamical gluon mass generation?