Ruling out some predictions of deeply-bound light-heavy tetraquarks using lattice QCD

We discuss our lattice QCD calculations of a number of tetraquark channels with at least one heavy quark where some phenomenological models, already fully constrained by fits to the ordinary meson and baryon spectrum, predict deep binding. We find no evidence of deeply-bound tetraquarks, except in previously established strong-interaction stable $I=0$, $J^P=1^+$, $ud\bar{b}\bar{b}$ and $I=1/2$, $J^P=1^+$ $\ell s\bar{b}\bar{b}$ (where $\ell=u/d$) channels, allowing us to rule out models predicting deep binding. Preliminary results from an updated analysis of doubly-bottom tetraquarks are also presented.