Summary
We perform an ${n}_{f}=2+1$ lattice study of a number of channels where past claims exist in the literature for the existence of strong-interaction-stable light-heavy tetraquarks. We find no evidence for any such deeply bound states, beyond the ${J}^{P}={1}^{+}$, $I=0$ $ud\overline{b}\overline{b}$ and $I=1/2$ $\ensuremath{\ell}s\overline{b}\overline{b}$ states already identified in earlier lattice studies. We also describe a number of systematic improvements to our previous lattice studies, including working with larger ${m}_{\ensuremath{\pi}}L$ to better suppress possible finite volume effects, employing extended sinks to better control excited-state contamination, and expanding the number of operators used in the GEVP analyses. Our results also allow us to rule out several phenomenologic
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