Tuning Fermilab heavy quarks in 2+1 flavor lattice QCD with application to hyperfine splittings

We report the nonperturbative tuning of parameters-kappa(c), kappa(b), and kappa(crit)-that are related to the bare heavy-quark mass in the Fermilab action. This requires the computation of the masses of D-s(*) B-s(*) and mesons comprised of a Fermilab heavy quark and a staggered light quark. Additionally, we report the hyperfine splittings for D-s(*) and B-s(*) mesons as a cross-check of our simulation and analysis methods. We find a splitting of 145 +/- 15 MeV for the D-s system and 40 +/- 9 MeV for the Bs system. These are in good agreement with the Particle Data Group average values of 143: 9 +/- 0: 4 MeV and 46: 1 +/- 1.5 MeV, respectively. The calculations are carried out with the MILC 2 + 1 flavor gauge configurations at three lattice spacings a approximate to 0: 15, 0.12, and 0.09 fm.