Tetraquark systems $\bar{b}b\bar{d}u$ in the static limit and lattice QCD

Abstract

Two hadrons with exotic quark content $Z_b^{+}\simeq \bar{b}b\bar{d}u$ were discovered by Belle. We present a lattice study of the $\bar{b}b\bar{d}u$ systems with various quantum numbers using static bottom quarks. Only one set of quantum numbers that couples to $Z_b$ and ${\rm Y}\pi$ was explored on the lattice before; these studies found an attractive potential between $B$ and ${\bar{B}}^{\ast }$ resulting in a bound state below the threshold. The present study considers the other three sets of quantum numbers. Eigenenergies of the $\bar{b}b\bar{d}u$ system are extracted as a function of separation between $b$ and $\bar{b}$. The resulting eigenenergies do not show any sizable deviation from noninteracting energies of the systems $\bar{b}b+\bar{d}u$ and $\bar{b}u+\bar{d}b$, so no significant attraction or repulsion is found. A slight exception is a small attraction between $B$ and ${\bar{B}}^{\ast }$ at small distance for the quantum number that couples to $Z_b$ and ${\eta }_b\rho$.

8 pages, 9 figures, one sign in operator O1 of equation (4) corrected, the sign in the calculation was correct

References in corpus (12)

• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• Amplitude analysis of e+e- => Y(nS)pi+pi- at sqrt(s)=10.865 GeV
• The Born-Oppenheimer approximation in an effective field theory language
• Study of the $B{\bar{B}}^{\ast }/D{\bar{D}}^{\ast }$ bound states in a Bethe-Salpeter approach
• Study of $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states
• Low energy chiral constants from epsilon-regime simulations with improved Wilson fermions
• $Z_b(10610)$ and $Z_b^{\prime }(10650)$ decays in a covariant quark model
• A mixing model for bottomoniumlike $Z_b$ resonances

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• Towards a Stringy Description for the $Q\bar{Q}q\bar{q}$-Quark System
• $QQqq\bar{q}$ Quark System, Compact Pentaquark, and Gauge/String Duality
• Bottomonium-like tetraquarks in a chiral quark model
• Unravelling Pentaquarks with Born--Oppenheimer effective theory
• Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory
• Electromagnetic properties of the $T_{cc}^{+}$ molecular states
• QCD confronts heavy-flavor and exotic hadrons
• Exotic hadrons associated with $b$-quark