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 ${\eta }_b\rho$.

arXiv comment8 pages, 9 figures, one sign in operator O1 of equation (4) corrected, the sign in the calculation was correct

References in corpus (32)

• Observation of two charged bottomonium-like resonances in Y(5S) decays
• 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
• Heavy quark spin structure in Z_b resonances
• Ab Initio Study of Hybrid b-bar-gb Mesons
• Born-Oppenheimer Approximation for the XYZ Mesons
• Coupled channel analysis of the rho meson decay 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
• Lattice QCD and Three-particle Decays of Resonances
• Tetraquark Interpretation of the Charged Bottomonium-like states Z_b^+-(10610) and Z_b^+-(10650) and Implications
• 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
• Hybridized Tetraquarks
• The Born-Oppenheimer approximation in an effective field theory language
• Hadro-quarkonium from Lattice QCD
• Interplay of quark and meson degrees of freedom in near-threshold states: A practical parametrisation for line shapes
• First Observation of the Zb0(10610) in a Dalitz Analysis of Y(5S) -> Y(nS) pi0 pi0
• Spin structure of heavy-quark hybrids
• Study of the $B{\bar{B}}^{\ast }/D{\bar{D}}^{\ast }$ bound states in a Bethe-Salpeter approach
• The line shapes of the $Z_b(10610)$ and $Z_b(10650)$ in the elastic and inelastic channels revisited
• 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
• General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions
• Low energy chiral constants from epsilon-regime simulations with improved Wilson fermions
• QCD spin effects in the heavy hybrid potentials and spectra
• Nonrelativistic effective field theory for heavy exotic hadrons
• Spin partners of the $Z_b(10610)$ and $Z_b(10650)$ revisited
• Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation
• The strong decay patterns of $Z_c$ and $Z_b$ states in the relativized quark model
• $Z_b(10610)$ and $Z_b^{\prime }(10650)$ decays in a covariant quark model
• Investigation of $B\bar{B}$ four-quark systems using lattice QCD
• A mixing model for bottomoniumlike $Z_b$ resonances

Cited by in corpus (12)

• 50 Years of Quantum Chromodynamics
• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Heavy meson thresholds in Born-Oppenheimer Effective field theory
• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
• 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