Abstract:We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the Λ QCD scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that α s (q 2 ) → 0 as q 2 → 0.
We construct the Pomeron as an exchange of two nonperturbative gluons, where the nonperturbative gluon propagator is described by an approximate solution of the Schwinger-Dyson equation which contains a dynamically generated gluon mass. We compute the total and elastic differential (der/dt) cross sections for pp scattering, obtaining agreement with the experimental data for a gluon mass m = 370 MeV for AgcD --300 MeV
We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the β function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.
We compute the tree level cross section for gluon-gluon elastic scattering taking into account a dynamical gluon mass, and show that this mass scale is a natural regulator for this subprocess cross section. Using an eikonal approach in order to examine the relationship between this gluon-gluon scattering and the elastic pp andpp channels, we found that the dynamical gluon mass is of the same order of magnitude as the ad hoc infrared mass scale m 0 underlying eikonalized QCD-inspired models. We argue that this correspondence is not an accidental result, and that this dynamical scale indeed represents the onset of nonperturbative contributions to the elastic hadron-hadron scattering. We apply the eikonal model with a dynamical infrared mass scale to obtain predictions for σ pp,pp tot , ρ pp,pp , slope B pp,pp , and differential elastic scattering cross section dσp p /dt at Tevatron and CERN-LHC energies.
We compare phenomenological values of the frozen QCD running coupling constant (␣ s ) with two classes of infrared finite solutions obtained through nonperturbative Schwinger-Dyson equations. We use these same solutions with frozen coupling constants as well as their respective nonperturbative gluon propagators to compute the QCD prediction for the asymptotic pion form factor. Agreement between theory and experiment on ␣ s (0) and F (Q 2 ) is found only for one of the Schwinger-Dyson equation solutions.
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