Study of isoscalar scalar bc u d tetraquark T₁₂ from lattice QCD

We present a lattice QCD study of the elastic S-wave DB scattering in search of tetraquark candidates with explicitly exotic flavor content bc u d in the isospin I\!=\!0 and JP=0^+ channel. We use four lattice QCD ensembles with dynamical u/d, s, and c quark fields generated by the MILC Collaboration. A non-relativistic QCD Hamiltonian, including improvement coefficients up to O (ₛv⁴), is utilized for the bottom quarks. For the rest of the valence quarks we employ a relativistic overlap action. Five different valence quark masses are utilized to study the light quark mass dependence of the DB scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic DB scattering amplitudes are extracted employing L\"uscher's prescription. The light quark mass dependence of the continuum extrapolated amplitudes suggests an attractive interaction between the B and D mesons. At the physical pseudoscalar meson mass (M₏ₒ=M_) the DB scattering amplitude has a sub-threshold pole corresponding to a binding energy of -39 (^+4-₆) (^~+8-₁₈) ~MeV with respect to the DB threshold. The critical M₏ₒ at which the DB scattering length diverges and the system becomes unbound corresponds to M^*₏ₒ=2. 94 (15) (5) ~GeV. This result can hold significant experimental relevance in the search for a bound scalar T₁₂ tetraquark, which could well be the next "doubly heavy" bound tetraquark to be discovered with only weak decay modes.