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, m₀, ζ, and cB=cE, 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 24³×48 sites and a coarse, 1/a=3.6 GeV, 16³×32 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: m₀, ζ, cB, and cE. 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 cE=cB is permitted through order a|→p| and to all orders in $ma$ where →p is the heavy quark's spatial momenta.