$bb\bar{u}\bar{d}$ and $bs\bar{u}\bar{d}$ tetraquarks from lattice QCD using two-meson and diquark-antidiquark variational basis

Abstract

We present a lattice QCD investigation of isoscalar tetraquark systems involving bottom quarks with explicit flavor content $bb\bar{u}\bar{d}$ and $bs\bar{u}\bar{d}$. In the doubly bottom sector, the study focuses on axialvector $J^P=1^{+}$ quantum numbers, whereas in the $bs\bar{u}\bar{d}$ channel both axial vector $J^P=1^{+}$ and scalar $J^P=0^{+}$ quantum numbers are investigated in search of signatures for possible tetraquark bound states. The calculations are performed on four ensembles with dynamical quark fields up to the charm quark generated by the MILC Collaboration, with lattice spacings ranging from approximately 0.058 fm to 0.12 fm, and at different values of the valence light quark mass $m_{u/d}$, corresponding to pseudoscalar meson masses, $M_{ps}$=0.5, 0.6 and 0.7 GeV. The energy eigenvalues in the finite volume are determined by applying a variational procedure to correlation matrices constructed from two-meson interpolating operators and diquark-antidiquark operators. Continuum extrapolated elastic $S$-wave scattering amplitudes of $B{B}^{\ast }$, $K{B}^{\ast }$ and $KB$ are extracted from the ground state eigenenergies following a finite-volume analysis á la Lüscher. The chiral and continuum extrapolated binding energy estimates for the isoscalar axialvector doubly bottom tetraquark $T_{bb}$ from the extracted elastic $B{B}^{\ast }$ $S$-wave scattering amplitudes is found to be $\Delta E_{T_{bb}}(1^{+})=-116{(}_{-36}^{+30})$ MeV. In the $bs\bar{u}\bar{d}$, no statistically significant deviations were observed in the ground state energies from the respective elastic threshold energies, leading to no conclusive evidence for any bound states.

v3: 18 pages, 15 figures, 7 tables, Several text and tables corrections to improve clarity. Published in Phys.Rev.D. Results and conclusions unchanged

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