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 $f_{B_c}=0.427(6)\mathrm{GeV}$; $m_{B_c}=6.285(10)\mathrm{GeV}$ and $f_{{\eta }_b}=0.667(6)\mathrm{GeV}$. Our value for $f_{{\eta }_b}$ is within a few percent of $f_{{\rm Y}}$, 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 summarize current results on decay constants of gold-plated mesons.

• Received 5 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.074503