The static quark potential and scaling behavior of SU(3) lattice Yang-Mills theory

The potential between a static quark and antiquark in pure SU(3) Yang-Mills theory is evaluated non-perturbatively through computations on the lattice in the region from short to intermediate distances (0.05 fm < r < 0.8 fm). In the high energy regime the results are compared with the parameter-free prediction of perturbation theory obtained by solving the Renormalization Group equation at two and three loops. The choice of the renormalization scheme to define a running coupling turns out to be important for the accuracy of the perturbative prediction: by obtaining the running coupling through the force, perturbation theory is applicable up to alpha ~ 0.3, while from the static potential only up to alpha ~ 0.15. In the region where perturbation is supposed to be reliable, no large unexpected non-perturbative term is observed. In the second part of this work, universality and scaling behavior of different formulations of Yang-Mills theory on the lattice are discussed, in particular the Iwasaki and DBW2 actions. The deconfinement temperature T_c*r0 and the glueball masses (m_0++)*r0, (m_2++)*r0 are analyzed. Particular attention is dedicated to the violation of physical positivity which occur in these actions and the consequences in the extraction of physical quantities from Euclidean correlation functions.