Non-perturbatively Determined Relativistic Heavy Quark Action

We present a method to non-perturbatively determine the parameters of the onshell, 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 non-uniqueness 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.