Heavy-light meson decay constants and hyperfine splittings with the heavy-HISQ method

We compute ratios between the vector and pseudoscalar, and tensor and vector decay constants, and between hyperfine splittings for $D_{(s)}^{(\ast )}$ and $B_{(s)}^{(\ast )}$ mesons. We use the Highly Improved Staggered Quark (HISQ) action for all valence quarks, paired with the second generation MILC $n_f=2+1+1$ HISQ gluon field configurations. These include light sea quarks with $m_u=m_d\equiv m_l$ going down to the physical values, as well as physically tuned strange and charm sea quarks. We also use a HISQ valence heavy quark, with mass ranging from that of the $c$-quark up to very nearly that of the physical $b$-quark on the finest lattices, allowing us to map out the heavy-quark mass dependence of the decay constant and hyperfine splitting ratios.