Bound isoscalar axial-vector $bc\bar{u}\bar{d}$ tetraquark $T_{bc}$ from lattice QCD using two-meson and diquark-antidiquark variational basis

Abstract

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. The calculation is performed at four values of lattice spacing, ranging $\sim$0.058 to $\sim$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 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 $D{\bar{B}}^{\ast }$ 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 $D{\bar{B}}^{\ast }$ scattering length ($a_0$) suggests that at the physical pion mass $a_0^{phys}=+0.57{(}_{-5}^{+4})(17)$ fm, which clearly points to an attractive interaction between the $D$ and ${\bar{B}}^{\ast }$ mesons that is strong enough to host a real bound state $T_{bc}$, with a binding energy of $-43{(}_{-7}^{+6}){(}_{-24}^{+14})$ MeV with respect to the $D{\bar{B}}^{\ast }$ 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 $m_{u/d}^{\ast }$ corresponding to $M_{ps}^{\ast }=2.73(21)(19)$ GeV.

Comments: 8 pages, 6 figures, 1 table, plus supplemental material (4 pages, 5 figures, 1 table). v2: version accepted to be published in Physical Review Letters. Results and conclusions unchanged