Bound isoscalar axial-vector bcu̅d̅ 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 bcu̅d̅, isospin I=0, and axialvector J^P=1^+ quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging ∼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 DB̅^* 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 DB̅^* scattering length (a_0) suggests that at the physical pion mass a_0^phys = +0.57(^+4_-5)(17) fm, which clearly points to an attractive interaction between the D and B̅^* 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 DB̅^* 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.