We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content $bc\overline{u}\overline{d}$, isospin $I=0$, and axial-vector $J^P=1^{+}$ quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging from $\sim 0.058$ to $\sim 0.12\mathrm{fm}$, and at five different values of valence light quark mass $m_{u/d}$, corresponding to pseudoscalar meson mass $M_{\mathrm{ps}}$ of about 0.5, 0.6, 0.7, 1.0, and 3.0 GeV. The energy eigenvalues in the finite volume are determined through a variational procedure applied to correlation matrices built out of two-meson interpolating operators as well as diquark-antidiquark operators. The continuum limit estimates for $D{\overline{B}}^{*}$ elastic $S$-wave scattering amplitude are extracted from the lowest finite-volume eigenenergies, corresponding to the ground states, using amplitude parametrizations supplemented by a lattice spacing dependence. Light quark mass $m_{u/d}$ dependence of the $D{\overline{B}}^{*}$ scattering length ($a_0$) suggests that at the physical pion mass $a_0^{\mathrm{phys}}=+0.57{(}_{-5}^{+4})(17)\mathrm{fm}$, which clearly points to an attractive interaction between the $D$ and ${\overline{B}}^{*}$ mesons that is strong enough to host a real bound state $T_{bc}$, with a binding energy of $-43{(}_{-7}^{+6}){(}_{-24}^{+14})\mathrm{MeV}$ with respect to the $D{\overline{B}}^{*}$ 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 $M_{\mathrm{ps}}^{*}=2.73(21)(19)\mathrm{GeV}$.

• Received 11 September 2023
• Revised 1 April 2024
• Accepted 19 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.201902

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Published by the American Physical Society