Lattice predictions for bound heavy tetraquarks

We investigate the possibility of doubly heavy qq′Q¯Q¯′ tetraquark bound states using n_f = 2+1 lattice QCD with pion masses ≃ 164, 299 and 415 MeV. Two types of lattice interpolating operator are chosen, reflecting first diquark-antidiquark and second meson-meson structure. Performing variational analyses 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 udb¯b¯, ℓsb¯b¯ as well as udc¯b¯, channels with ℓ = u,d. In the case of the udb¯b¯ and ℓsb¯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 not only strong-interaction, but also electromagnetic-interaction stable, and can decay only weakly. So far these are the first exotic hadrons predicted to have this feature. Further evidence for binding is found in the udc¯b¯ channel, where the binding energy broadly straddles the electromagnetic stability threshold. We also study the dependence of the tetraquark binding on heavy quark mass by considering the channels udb¯′b¯′, ℓsb¯′b¯′ as well as udb¯′b¯, ℓsb¯′b¯ involving a heavy b′ quark with mass between roughly 0.6 and 6.3 times the physical b quark mass. The observed mass dependence of these four flavor channels is shown to follow closely a phenomenological form expected on simple physical grounds.