PROBLEMS WITH THE EUCLIDEAN FORMULATION OF HEAVY QUARK EFFECTIVE THEORIES

We discuss the formulation in euclidean space of the effective theory for heavy quarks at non-zero velocity, which is necessary for the implementation of the Isgur-Wise limit in lattice QCD simulations. In this theory the energy spectrum is unbounded from below and, even at the tree level, an ultraviolet cut-off on spatial momenta must be introduced. The continuum limit of the effective quark propagator in configuration space does not exist. It is however possible, at least in the non-interacting case, to construct sensible correlation functions in time and in spatial momenta. The application of the theory to lattice simulations seems very problematic.