Bound isoscalar axial-vector $bc\bar u\bar d$ tetraquark $T_{bc}$ in QCD
We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content $bc\bar u\bar d$, isospin $I\!=\!0$, and axialvector $J^P=1^+$ quantum numbers in search of possible tetraquark bound states. We employ four lattice QCD ensembles with dynamical $u/d$, $s$, and $c$ quark fields, generated by the MILC Collaboration with a highly improved staggered quark fermion action. The valence quarks, with quark masses ranging from light to the charm sector, are implemented using an overlap action. For bottom quark we use a nonrelativistic QCD Hamiltonian, including improvement coefficients up to $\mathcal{O}(\alpha_sv^4)$. The calculation is performed at four values of lattice spacing, ranging in between of about 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 finite-volume energy spectra are determined through a variational procedure applied to correlation matrices built out of two-meson interpolating operators as well as local diquark-antidiquark operators. We perform global fits to the lattice extracted $DB^*$ scattering amplitude, supplemented by terms describing discretization effects and $m_{u/d}$ dependence, then extrapolate the lattice spacing to zero and $m_{u/d}$ to its physical value. The $DB^*$ scattering length at the physical $M_{ps}$ is found to be $a_0^{phys} = +0.57(^{+4}_{-5})(17)$ fm, which clearly points to an attractive interaction between the $D$ and $B^*$ mesons that is strong enough to host a real bound state $T_{bc}$, $43(^{+7}_{-6})(^{+24}_{-14})$ MeV below the $DB^*$ 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 $M^{*}_{ps} = 2.73(21)(14)$ GeV.