We determine masses and decay constants of heavy-heavy and heavy-charm
pseudoscalar mesons as a function of heavy quark mass using a fully
relativistic formalism known as Highly Improved Staggered Quarks for the heavy
quark. We are able to cover the region from the charm quark mass to the bottom
quark mass using MILC ensembles with lattice spacing values from 0.15 fm down
to 0.044 fm. We obtain f_{B_c} = 0.427(6) GeV; m_{B_c} = 6.285(10) GeV and
f_{\eta_b} = 0.667(6) GeV. Our value for f_{\eta_b} is within a few percent of
f_{\Upsilon} confirming that spin effects are surprisingly small for heavyonium
decay constants. Our value for f_{B_c} is significantly lower than potential
model values being used to estimate production rates at the LHC. We discuss the
changing physical heavy-quark mass dependence of decay constants from
heavy-heavy through heavy-charm to heavy-strange mesons. A comparison between
the three different systems confirms that the B_c system behaves in some ways
more like a heavy-light system than a heavy-heavy one. Finally we summarise
current results on decay constants of gold-plated mesons.Comment: 16 pages, 12 figure
