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 $-39(^{+4}_{-6})(^{~+8}_{-18}) \mbox{~MeV}$ 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.

13 pages, 10 figures

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Cited by in corpus (10)

• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
• $bb\bar{u}\bar{d}$ and $bs\bar{u}\bar{d}$ tetraquarks from lattice QCD using two-meson and diquark-antidiquark variational basis
• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• Structure of open-flavour four-quark states in the charm and bottom region
• Precise study of triply charmed baryons ${\Omega }_{ccc}$
• $D^{(\ast )}{\bar{B}}^{(\ast )}$ dynamics in chiral effective field theory
• Prediction of an $I(J^P)=0(1^{-})$ $\bar{b}\bar{b}ud$ Tetraquark Resonance Close to the $B^{\ast }{B}^{\ast }$ Threshold Using Lattice QCD Potentials
• Lattice QCD Study of Positive Parity Dibaryons with Maximal Charm and Strangeness
• Meson scattering and tetraquarks in two-dimensional QCD
• Exotic hadrons associated with $b$-quark