Non-perturbatively determined relativistic heavy quark action

Preliminary results are presented in a step scaling determination of the coefficients in the relativistic heavy quark action. By matching finite volume, heavy-heavy and heavy-light meson masses, we attempt to determine the four parameters ($m$, $\zeta$, $c_B$ and $c_E$) in the on-shell-improved, heavy quark action. In this report we carry out one step in this program by matching two physically equivalent systems. The first is a fully relativistic calculation using a $24^3\times 48$, $1/a=5.4$ GeV lattice with both the heavy and light quarks treated as domain wall fermions. The second calculation uses at $16^3\times 32$, $1/a=3.6$ GeV lattice, a domain-wall light quark and a heavy quark computed with the relativistic heavy quark action. The four parameters in this heavy quark effective action are then varied to reproduce the mass spectrum from the first calculation. These calculations are carried out in the quenched approximation for a heavy quark mass approximately that of the charmed quark