  We present a lattice QCD study of the elastic $S$-wave $D\bar{B}$ scattering
in search of tetraquark candidates with explicitly exotic flavor content
$bc\bar u\bar d$ in the isospin $I\!=\!0$ and $J^P=0^+$ 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 $\mathcal{O}(\alpha_sv^4)$, 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 $D\bar{B}$ scattering amplitude. The finite
volume energy spectra are extracted following a variational approach. The
elastic $D\bar{B}$ 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 $\bar B$ and $D$
mesons. At the physical pseudoscalar meson mass ($M_{ps}=M_{\pi}$) the
$D\bar{B}$ scattering amplitude has a sub-threshold pole corresponding to a
binding energy of $-39(^{+4}_{-6})(^{~+8}_{-18}) \mbox{~MeV}$ with respect to
the $D\bar{B}$ threshold. The critical $M_{ps}$ at which the $D\bar{B}$
scattering length diverges and the system becomes unbound corresponds to
$M^*_{ps}=2.94(15)(5) \mbox{~GeV}$. This result can hold significant
experimental relevance in the search for a bound scalar $T_{bc}$ tetraquark,
which could well be the next "doubly heavy" bound tetraquark to be discovered
with only weak decay modes.
