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We report a lattice QCD study of the heavy-light meson-meson interactionswith an explicitly exotic flavor content $bc\bar u\bar d$, isospin $I\!=\!0$,and axialvector $J^P=1^+$ quantum numbers in search of possible tetraquarkbound states. We employ four lattice QCD ensembles with dynamical $u/d$, $s$,and $c$ quark fields, generated by the MILC Collaboration with a highlyimproved staggered quark fermion action. The valence quarks, with quark massesranging from light to the charm sector, are implemented using an overlapaction. For bottom quark we use a nonrelativistic QCD Hamiltonian, includingimprovement coefficients up to $\mathcal{O}(\alpha_sv^4)$. The calculation isperformed at four values of lattice spacing, ranging in between of about 0.058to 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 avariational procedure applied to correlation matrices built out of two-mesoninterpolating operators as well as local diquark-antidiquark operators. Weperform 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 itsphysical value. The $DB^*$ scattering length at the physical $M_{ps}$ is foundto be $a_0^{phys} = +0.57(^{+4}_{-5})(17)$ fm, which clearly points to anattractive interaction between the $D$ and $B^*$ mesons that is strong enoughto host a real bound state $T_{bc}$, $43(^{+7}_{-6})(^{+24}_{-14})$ MeV belowthe $DB^*$ threshold. We also find that the strength of the binding decreaseswith increasing $m_{u/d}$ and the system becomes unbound at a critical lightquark mass $m^{*}_{u/d}$ corresponding to $M^{*}_{ps} = 2.73(21)(14)$ GeV.

Bound isoscalar axial-vector $bc\bar u\bar d$ tetraquark $T_{bc}$ in QCD