The Transition from Nonperturbative to Perturbative QCD

Lattice-based investigations of two fundamental QCD quantities are described, namely the gluon and quark propagators in Landau gauge. We have studied the Landau gauge gluon propagator using a variety of lattices with spacings from a = 0.17 to 0.41 fm to explore finite volume and discretization effects. We also introduce the general method of "tree-level correction" to minimize the effect of lattice artefacts at large momenta. We demonstrate that it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings and to explore the infinite volume and continuum limits of the Landau-gauge gluon propagator. These results confirm the earlier conclusion that the Landau gauge gluon propagator is infrared finite. We study the Landau gauge quark propagator in quenched QCD using two forms of the {\cal O}( a ; )-improved propagator with the Sheikholeslami-Wohlert quark action with the nonperturbative value for the clover coefficient c_sw and mean-field improvement coefficients in our improved quark propagators. We again implement an appropriate form of tree-level correction. We find good agreement between our improved quark propagators. The extracted value of infrared quark mass in the chiral limit is found to be 300 ± 30 MeV. We conclude that the momentum regime where the transition from nonperturbative to perturbative QCD occurs is Q² ≃ 4 GeV².