Bound Isoscalar Axial-Vector bcu[over ¯]d[over ¯] Tetraquark T_{bc} from Lattice QCD Using Two-Meson and Diquark-Antidiquark Variational Basis

We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content bcu[over ¯]d[over ¯], isospin I=0, and axial-vector J^{P}=1^{+} quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging from ∼0.058 to ∼0.12  fm, and at five different values of valence light quark mass m_{u/d}, corresponding to pseudoscalar meson mass M_{ps} of about 0.5, 0.6, 0.7, 1.0, and 3.0 GeV. The energy eigenvalues in the finite volume are determined through a variational procedure applied to correlation matrices built out of two-meson interpolating operators as well as diquark-antidiquark operators. The continuum limit estimates for DB[over ¯]^{*} elastic S-wave scattering amplitude are extracted from the lowest finite-volume eigenenergies, corresponding to the ground states, using amplitude parametrizations supplemented by a lattice spacing dependence. Light quark mass m_{u/d} dependence of the DB[over ¯]^{*} scattering length (a_{0}) suggests that at the physical pion mass a_{0}^{phys}=+0.57(_{-5}^{+4})(17)  fm, which clearly points to an attractive interaction between the D and B[over ¯]^{*} mesons that is strong enough to host a real bound state T_{bc}, with a binding energy of -43(_{-7}^{+6})(_{-24}^{+14})  MeV with respect to the DB[over ¯]^{*} threshold. We also find that the strength of the binding decreases with increasing m_{u/d} and the system becomes unbound at a critical light quark mass m_{u/d}^{*} corresponding to M_{ps}^{*}=2.73(21)(19)  GeV.

Lattice Evidence for Bound Heavy Tetraquarks

We investigate the possibility of qq'$ \bar {Q}\bar {Q}' $ tetraquark bound states using nf = 2 + 1 lattice QCD with pion masses ≃ 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} $, ℓs$ \bar {b}\bar {b} $ as well as ud$ \bar {c}\bar {b} $, channels with ℓ= u, d. In the case of the ud$ \bar {b}\bar {b} $ and ℓs$ \bar {b}\bar {b} $ channels unambiguous signals for JP=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} $, ℓs$ \bar {Q}\bar {Q} $ as well as ud$ \bar {Q}\bar {b} $, ℓs$ \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.