Soft covariant gauges on the lattice.

In recent years, hadron spectroscopy has become the most popular field of application of lattice QCD. Hadron masses, decay constants, and matrix elements for semileptonic decays are routinely computed from Green functions of composite hadron fields and expectation values of current operators between hadron states. However, the predictive power of lattice QCD is not limited to these kinds of calculations. In particular, Green functions of individual quark and gluon fields can be computed as well as expectation values of operators between quark and gluon states. The interest of this approach is twofold. Firstly, one can compute nonperturbatively renormalization constants for composite operators by sandwiching them between quark states @1#. These calculations form a crucial step in extracting physical information from lattice calculations. Secondly, quark and gluon Green functions are interesting objects in their own right. Being the most fundamental computable quantities in QCD, they are expected to contain direct information on the mechanism of color confinement and chiral symmetry breaking. Also, they allow a direct determination from first principles of the running QCD coupling @2# and may be relevant for understanding the physics of Pomeron exchange from the point of view of QCD @3#. Unlike hadronic operators, Green functions for quark and gluons must be defined in a fixed gauge. For most of the applications described above, it is a crucial problem to disentangle gauge-dependent features from gauge independent ones. For example, if a dynamical mass were extracted from a nonperturbative study of the gluon propagator, a physical interpretation may be attached to it only if one can obtain reasonable evidence that such a mass does not depend on the gauge chosen, at least within a class of gauges. For this reason, it would be of great interest to be able to define and implement on the lattice a whole family of nonperturbative gauge conditions, by varying continously some gauge parameter. In this paper we describe a numerical study of one such class of gauges. In Sec. II we recall the formulation of the gauge condition, in the framework of the Feynman path integral, and the corresponding Monte Carlo algorithm. In Sec.