Gluon and Ghost Propagators in Landau Gauge on the Lattice

Abstract

We study the ultraviolet behaviour of the ghost and gluon propagators in quenched QCD using lattice simulations. Extrapolation of the lattice data towards the continuum allows to use perturbation theory to extract $Λ_{\text{QCD}}$ - the fundamental parameter of the pure gauge theory. The values obtained from the ghost and gluon propagators are coherent. The result for pure gauge SU(3) at three loops is $Λ_{\ms}\approx 320\text{MeV}$. However this value does depend strongly upon the order of perturbation theory and upon the renormalisation description of the continuum propagators. Moreover, this value has been obtained without taking into account possible power corrections to the short-distance behaviour of correlation functions.