On lattice actions for static quarks

We introduce new discretizations of the action for static quarks. They achieve an exponential improvement (compared to the Eichten-Hill regularization) on the signal to noise ratio in static-light correlation functions. This is explicitly checked in a quenched simulation and it is understood quantitatively in terms of the self energy of a static quark and the lattice heavy quark potential at zero distance. We perform a set of scaling tests in the Schroedinger functional and find scaling violations in the O(a) improved theory to be rather small -- for one observable significantly smaller than with the Eichten-Hill regularization. In addition we compute the improvement coefficients of the static light axial current up to O(g_0^4) corrections and the corresponding renormalization constants non-perturbatively. The regularization dependent part of the renormalization of the b-quark mass in static approximation is also determined