Maximal variance reduction for stochastic propagators with applications to the static quark spectrum

We study a new method—maximal variance reduction—for reducing the variance of stochastic estimators for quark propagators. We find that while this method is comparable to the usual iterative inversion for light-light mesons, a considerable improvement is achieved for systems containing at least one infinitely heavy quark. Such systems are needed for heavy quark effective theory. As an illustration of the effectiveness of the method we present results for the masses of the ground state and excited states of $\overline{Q}q$ mesons and $\overline{Q}\mathrm{qq}$ baryons. We compare these results with the experimental spectra involving $b$ quarks.