Study of isoscalar scalar $bc\bar{u}\bar{d}$ tetraquark $T_{bc}$ from lattice QCD

Abstract

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 $\mathcal{O}({\alpha }_s{v}^4)$, 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 Lüscher'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 $-39{(}_{-6}^{+4}){(}_{-18}^{+8})\text{mbox}MeV$ 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 $M_{ps}^{\ast }=2.94(15)(5)\text{mbox}GeV$. 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.

Comments: 13 pages, 10 figures