We report on a calculation of $B_c$ ground state and radial excitation energies, obtained from heavy-charm highly improved staggered quark (HISQ) correlators computed on MILC gauge ensembles, with lattice spacings down to $a=0.044$ fm. Using HISQ valence quarks on progressively finer lattices allows us to simulate up to the $b$-quark mass.
In particular we focus on the $B_c(2S)$ energy, which we compare with $O(\alpha_s$)-improved non-relativistic QCD results computed on the same ensembles and recent experimental results from ATLAS.