On lattice actions for static quarks

We introduce new discretizations of the action for static quarks. Theyachieve an exponential improvement (compared to the Eichten-Hillregularization) on the signal to noise ratio in static-light correlationfunctions. This is explicitly checked in a quenched simulation and it isunderstood quantitatively in terms of the self energy of a static quark and thelattice heavy quark potential at zero distance. We perform a set of scalingtests in the Schroedinger functional and find scaling violations in the O(a)improved theory to be rather small -- for one observable significantly smallerthan with the Eichten-Hill regularization. In addition we compute theimprovement 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 instatic approximation is also determined.Comment: 30 pages, 9 figure