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

We present a lattice QCD study of the elastic S-wave DB̄ 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(αₛv⁴), 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 DB̄ scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic DB̄ scattering amplitudes are extracted employing L\"{u}scher'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 (Mₚₛ=Mπ) the DB̄ scattering amplitude has a sub-threshold pole corresponding to a binding energy of -39(⁺⁴₋₆)(~+8₋₁₈) ~MeV with respect to the DB̄ threshold. The critical Mₚₛ at which the DB̄ scattering length diverges and the system becomes unbound corresponds to M^*ₚₛ=2.94(15)(5) ~GeV. This result can hold significant experimental relevance in the search for a bound scalar Tbc tetraquark, which could well be the next "doubly heavy" bound tetraquark to be discovered with only weak decay modes.