Lattice Evidence for Bound Heavy Tetraquarks

We investigate the possibility of $qq'\bar{Q}\bar{Q}'$ tetraquark bound states using $n_f = 2 + 1$ lattice QCD with pion masses $\simeq 164, 299$ and 415 MeV. Two types of lattice interpolating operator are chosen, reflecting first diquarkantidiquark and second meson-meson structure. Performing variational analysis using these operators and their mixings, we determine the ground and first excited states from the lattice correlators. Using non-relativistic QCD to simulate the bottom quarks and the Tsukuba formulation of relativistic heavy quarks for charm quarks, we study the $ud\bar{b}\bar{b}$, $\ell s\bar{b}\bar{b}$ as well as $ud\bar{c}\bar{b}$, channels with $\ell = u, d$. In the case of the $ud\bar{c}\bar{b}$ and $\ell s\bar{b}\bar{b}$ channels unambiguous signals for $J^P = 1^+$ tetraquarks are found with binding energies 189(10) and 98(7) MeV below the corresponding free two-meson thresholds at the physical point. These tetraquarks are therefore strong-interaction stable, implying they are stable under strong as well as electromagnetic interactions while they can decay weakly. So far these are the first exotic hadrons predicted to have this feature. Further evidence for binding is found in the $ud\bar{c}\bar{b}$ channel, whereby the binding energy broadly straddles the electromagnetic stability threshold. Studying further the quark mass dependence we vary the heavy quark mass in $ud\bar{Q}\bar{Q}$, $\ell s\bar{Q}\bar{Q}$ as well as $ud\bar{Q}\bar{b}$, $\ell s\bar{Q}\bar{b}$ between roughly 0.7 and 6.3 times the bottom quark mass. The observed mass dependence of these four flavor channels closely follows a behaviour argued from phenomenological considerations of the heavy baryon spectrum.