CONSISTENCY AND LATTICE RENORMALIZATION OF THE EFFECTIVE THEORY FOR HEAVY QUARKS

The effective theory describing infinite mass particles with fixed velocity has the unpleasant characteristic that the energy spectrum is unbounded from below; this fact is the source of difficulties in formulating the euclidean theory. We present in this work an analysis of the euclidean effective theory and demonstrate that, in spite of its unbounded spectrum, the theory is consistent. Moreover, a technique for the perturbative evaluation of the amplitudes is described. We also compute the one-loop renormalization constants of the lattice effective theory, and of the heavy-heavy current needed for the determination of the Isgur-Wise function. A variety of effects related to the explicit breaking of the Lorentz symmetry of the lattice regularization are also shown. Among the most peculiar phenomena is a finite renormalization of the heavy quark velocity. Finally, we compute the lattice-continuum renormalization constant of the Isgur-Wise current, which is needed for the conversion of the values of the matrix elements computed with the lattice effective theory to the values in the full theory.