Exotic $B_s$ mesons in the continuum from a nonperturbatively-tuned heavy quark action
In this work we predict the masses and binding energies of two $B_s$ exotic-meson candidates using Lattice QCD, namely the $B_{s0}^*$ and $B_{s1}$. We use a relativistic heavy-quark action for the valence b-quark in our simulations, tuned fully non-perturbatively by a neural network. This allows us to take the continuum limit and eliminates the largest systematic we attributed to our previous determination of these states using Lattice-NRQCD. This is the first Lattice QCD study to show that these states remain deeply bound in the continuum limit. We thoroughly benchmark our heavy-quark approach by reproducing the experimental values of the 1S hyperfine splittings of $B$ and $B_s$ mesons, as well as the mass splitting between the $B$ and $B_s$ mesons. Our final results yield binding energies with respect to the $BK$ and $B^*K$ thresholds of $-65.9(6.0)(3.0)_\text{Iso}$ MeV and $-60.6(6.6)(3.0)_\text{Iso}(1.0)_\text{GEVP}$ MeV for the $B_{s0}^*$ and $B_{s1}$ respectively.