Nonperturbatively determined relativistic heavy quark action

We present a method to nonperturbatively determine the parameters of the on-shell, O(a)-improved relativistic heavy quark action. These three parameters, m{sub 0}, {zeta}, and c{sub B}=c{sub E}, are obtained by matching finite-volume, heavy-heavy, and heavy-light meson masses to the exact relativistic spectrum through a finite-volume, step-scaling recursion procedure. We demonstrate that accuracy on the level of a few percent can be achieved by carrying out this matching on a pair of lattices with equal physical spatial volumes but quite different lattice spacings. A fine lattice with inverse lattice spacing 1/a=5.4 GeV and 24{sup 3}x48 sites and a coarse, 1/a=3.6 GeV, 16{sup 3}x32 lattice are used together with a heavy quark mass m approximately that of the charm quark. This approach is unable to determine the initially expected, four heavy quark parameters: m{sub 0}, {zeta}, c{sub B}, and c{sub E}. This apparent nonuniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction c{sub E}=c{sub B} is permitted through order a|p-vector| and to all orders in ma where p-vector is the heavy quark's spatial momenta.