The Infrared Behaviour of the Running Coupling in Landau Gauge QCD 1

Approximate solutions for the gluon and ghost propagators as well as the running coupling in Landau gauge Yang–Mills theories are presented. These propagators obtained from the corresponding Dyson–Schwinger equations are in remarkable agreement with those of recent lattice calculations. The resulting running coupling possesses an infrared fixed point, αS(0) = 8.92/Nc for all gauge groups SU(Nc). Above one GeV the running coupling rapidly approaches its perturbative form. The investigation of Quantum Chromo Dynamics (QCD) over the last decades made obvious that a description of hadrons and their processes from the dynamics of confined quarks and gluons in one coherent approach is an outstanding complicated task. Knowledge of a completely non-perturbative running coupling would be a very important step to make towards such a QCD-based description of hadrons. Given the experimental results in hadron physics it is evident that baryons and mesons are not elementary particles in the naive sense of the word " elementary ". The partonic substructure of the nucleon has been determined to an enormous precision leaving no doubt that the parton picture emerges from quarks and gluons, the elementary fields of QCD. This contrasts the well-known fact that these quarks and gluons have not been detected outside hadrons. This puzzle was given a name: confinement. The confinement hypothesis was formulated several decades ago, nevertheless, our understanding of the confinement mechanism(s) is still not satisfactory. Moreover, in contrast to other non-perturbative phenomena in QCD (e.g., dynamical breaking of