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.