One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium

Abstract

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the Born$-$Oppenheimer (BO) effective field theory (BOEFT), derived from Quantum Chromodynamics (QCD) on the basis of scale separation and symmetries, can address XYZ exotics of any composition. We derive the Schrödinger coupled equations that describe hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order, incorporating nonadiabatic terms, and present the predicted multiples. We define the static potentials in terms of the QCD static energies for all relevant cases. We provide the precise form of the nonperturbative low-energy gauge-invariant correlators required for the BOEFT: static energies, generalized Wilson loops, gluelumps, and adjoint mesons. These are to be calculated on the lattice and we calculate here their short-distance behavior. Furthermore, we outline how spin-dependent corrections and mixing terms can be incorporated using matching computations. Lastly, we discuss how static energies with the same BO quantum numbers mix at large distances leading to the phenomenon of avoided level crossing. This effect is crucial to understand the emergence of exotics with molecular characteristics, such as the ${\chi }_{c1}(3872)$. With BOEFT both the tetraquark and the molecular picture appear as part of the same description.

arXiv comment115 pages, 13 figures, 13 tables; v2: Minor updates, Journal version

References in corpus (140)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Heavy quarkonium: progress, puzzles, and opportunities
• Hadronic molecules
• Universality in Few-body Systems with Large Scattering Length
• Observation of $J/\psi p$ resonances consistent with pentaquark states in ${\Lambda }_b^0\to J/\psi K^{-}p$ decays
• Observation of a charged charmoniumlike structure in e+e- to pi+pi-J/psi at \sqrt{s}=4.26 GeV
• The $XYZ$ states: experimental and theoretical status and perspectives
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Diquark-Antidiquarks with Hidden or Open Charm and the Nature of X(3872)
• Pentaquark and Tetraquark states
• Heavy-Quark QCD Exotica
• Diquarks and Exotic Spectroscopy
• Study of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ and Observation of a Charged Charmonium-like State at Belle
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Potential NRQCD: an effective theory for heavy quarkonium
• Effective field theories for heavy quarkonium
• An updated review of the new hadron states
• Exotics: Heavy Pentaquarks and Tetraquarks
• Observation of two charged bottomonium-like resonances in Y(5S) decays
• Improved Nonrelativistic QCD for Heavy Quark Physics
• Observation of a resonance-like structure in the pi^+- psi' mass distribution in exclusive B-->K pi^+- psi' decays
• QCD and strongly coupled gauge theories: challenges and perspectives
• Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
• Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
• Observation of an exotic narrow doubly charmed tetraquark
• Observation of String Breaking in QCD
• Scattering processes and resonances from lattice QCD
• The D*0 D0bar threshold resonance
• The Exotic XYZ Charmonium-like Mesons
• Fine Structure of the QCD String Spectrum
• Hadro-Charmonium
• Multiquark States
• Static potentials and glueball masses from QCD simulations with Wilson sea quarks
• Pion Interactions in the X(3872)
• Three-loop static potential
• Hybrid Mesons
• The infrared behaviour of the static potential in perturbative QCD
• 50 Years of Quantum Chromodynamics
• Study of doubly heavy tetraquarks in Lattice QCD
• Ab Initio Study of Hybrid b-bar-gb Mesons
• Observation of new resonances decaying to $J/\psi K^{+}$ and $J/\psi \varphi$
• Born-Oppenheimer Approximation for the XYZ Mesons
• Decay width of light quark hybrid meson from the lattice
• Static QCD potential at three-loop order
• Observation of a near-threshold structure in the $K^{+}$ recoil-mass spectra in $e^{+}{e}^{-}\to K^{+}(D_s^{-}{D}^{\ast 0}+D_s^{\ast -}{D}^0)$
• Observation of a new charged charmoniumlike state in B -> J/psi K pi decays
• Evidence of Two Resonant Structures in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$
• Suppressed decay into open charm for the Y(4260) being an hybrid
• Effective Field Theory Lagrangians for Baryons with Two and Three Heavy Quarks
• The QCD Potential at $O(1/m)$
• Heavy quarkonium suppression in a fireball
• Evidence for X(3872) from DD* scattering on the lattice
• QCD phenomenology of static sources and gluonic excitations at short distances
• Line Shapes of the X(3872)
• An explanation of Belle states Z_b(10610) and Z_b(10650)
• Evidence for a new resonance and search for the Y(4140) in $\gamma \gamma \to \varphi J/\psi$
• Observation of $Z_c(3900{)}^0$ in $e^{+}{e}^{-}\to {\pi }^0{\pi }^{0}J/\psi$
• Quarkonium Hybrids with Nonrelativistic Effective Field Theories
• Lattice QCD investigation of a doubly-bottom $\bar{b}\bar{b}ud$ tetraquark with quantum numbers $I(J^P)=0(1^{+})$
• BB interactions with static bottom quarks from Lattice QCD
• How the Z_c(3900) Reveals the Spectra of Quarkonium Hybrid and Tetraquark Mesons
• Hadrons with a heavy colour-adjoint particle
• The QCD potential at O(1/m^2): Complete spin-dependent and spin-independent result
• X(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD
• Study of the $Z_c^{+}$ channel using lattice QCD
• String breaking by light and strange quarks in QCD
• Inclusive Decays of Heavy Quarkonium to Light Particles
• Heavy Quarkonium Hybrids: Spectrum, Decay and Mixing
• Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
• Charmonium-like resonances with $J^{PC}=0^{++},2^{++}$ in coupled $D\bar{D}$, $D_s{\bar{D}}_s$ scattering on the lattice
• Decays of an exotic $1^{-+}$ hybrid meson resonance in QCD
• A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context
• The QCD static energy at NNNLL
• Precision computation of hybrid static potentials in SU(3) lattice gauge theory
• Masses of Doubly Heavy Tetraquarks with Error Bars
• Tetraquark bound states in the heavy-light heavy-light system
• The Born-Oppenheimer approximation in an effective field theory language
• The logarithmic contribution to the QCD static energy at NNNNLO
• One pion exchange and the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks
• First Observation of the Zb0(10610) in a Dalitz Analysis of Y(5S) -> Y(nS) pi0 pi0
• Spin structure of heavy-quark hybrids
• Effective range expansion for narrow near-threshold resonances
• Determination of the QCD coupling from the static energy and the free energy
• Long-range properties of $1S$ bottomonium states
• Observation of the $Y(4230)$ and a new structure in $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$
• Why Hybrid Meson Coupling to Two S-wave Mesons is Suppressed
• QCD spin effects in the heavy hybrid potentials and spectra
• On the scattering of D and D* mesons off the X(3872)
• Charged charmonium-like Z+(4430) from rescattering in conventional B decays
• Heavy Quarkonia: Wilson Area Law, Stochastic Vacuum Model and Dual QCD
• Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory
• The Hydrogen Bond of QCD in Doubly Heavy Baryons and Tetraquarks
• The three-quark static potential in perturbation theory
• Exotic to standard bottomonium transitions
• Nonrelativistic effective field theory for heavy exotic hadrons
• Effective string theory constraints on the long distance behavior of the subleading potentials
• The decay of the X(3872) into χ_{cJ} and the Operator Product Expansion in XEFT
• Regeneration of bottomonia in an open quantum systems approach
• Search for $\bar{b}\bar{b}us$ and $\bar{b}\bar{c}ud$ tetraquark bound states using lattice QCD
• Diabatic description of charmonium-like mesons
• Hybrid static potentials in SU(3) lattice gauge theory at small quark-antiquark separations
• Selection Rules for Hadronic Transitions of XYZ Mesons
• The Hydrogen Bond of QCD
• Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation
• Effective string theory and the long-range relativistic corrections to the quark-antiquark potential
• Decay and electromagnetic production of strongly coupled quarkonia in pNRQCD
• Shallow Bound States and Hints for Broad Resonances with Quark Content $\bar{b}\bar{c}ud$ in $B$-$\bar{D}$ and $B^{\ast }$-$\bar{D}$ Scattering from Lattice QCD
• Observation of the $Y(4230)$ and evidence for a new vector charmonium-like state $Y(4710)$ in $e^{+}{e}^{-}\to K_S^0{K}_S^{0}J/\psi$
• Inclusive production of $J/\psi$, $\psi (2S)$, and ${\rm Y}$ states in pNRQCD
• A lattice QCD study of generalized gluelumps
• Excited and exotic bottomonium spectroscopy from lattice QCD
• Effective field theory for double heavy baryons at strong coupling
• Tetraquark systems $\bar{b}b\bar{d}u$ in the static limit and lattice QCD
• Production and polarization of $S$-wave quarkonia in potential nonrelativistic QCD
• Symmetries of the Three Heavy-Quark System and the Color-Singlet Static Energy at NNLL
• Heavy hybrid decays to quarkonia
• Heavy Hybrid Decays in a Constituent Gluon Model
• Hyperfine splittings of heavy quarkonium hybrids
• A coupled-channel lattice study on the resonance-like structure $Z_c(3900)$
• Perturbative Corrections to Heavy Quark-Diquark Symmetry Predictions for Doubly Heavy Baryon Hyperfine Splittings
• Diabatic description of bottomoniumlike mesons
• Heavy-Quark spin symmetry breaking in the Born-Oppenheimer approximation
• Heavy meson thresholds in Born-Oppenheimer Effective field theory
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Colour octet potential to three loops
• Why quarkonium hybrid coupling to two S-wave heavy-light mesons is not suppressed
• Diabatic description of charmoniumlike mesons II: mass corrections and strong decay widths
• Charm and bottom baryons in nonperturbative quark dynamics
• Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons
• Evidence of a $J/\psi K_S^0$ structure in $B^0\to J/\psi \varphi K_S^0$ decays
• Exotic Hadrons from Scattering in the Diabatic Dynamical Diquark Model
• Eight very excited spectra and one possible axion in SU(3) lattice gauge theory
• Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory
• Baryons, multi-hadron systems, and composite dark matter in non-relativistic QCD
• Spectrum of very excited ${\Sigma }_g^{+}$ flux tubes in SU(3) gauge theory
• Effect of continuum states on the double-heavy hadron spectra
• Towards a Theoretical Understanding of the XYZ Mesons from QCD
• QCD confronts heavy-flavor and exotic hadrons

Cited by in corpus (16)

• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
• Unravelling Pentaquarks with Born--Oppenheimer effective theory
• Tetraquarks in the Born-Oppenheimer approximation
• A short review on the compositeness of the $X(3872)$
• Investigating hybrid mesons with $0^{+-}$ and $2^{+-}$ exotic quantum numbers
• $\lambda$ and $\rho$ Regge trajectories for the pentaquark $P_{cc\bar{c}bb}$ in the diquark-triquark picture
• 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
• Hybrid to Quarkonia transitions
• The $B^{-}\to J/\psi {\eta }^{\prime }{K}^{-}$ reaction and the $Y(4710)$ and $K_0^{\ast }(1430)$ contributions
• Hadronic molecules and multiquark states
• Systematic exploration of triply heavy tetraquarks: spectroscopic and decay characteristics
• Assessing the validity of the Born-Oppenheimer approximation in potential models for doubly heavy hadrons
• Binding energy of the $T_{bb}$ tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions
• Meson scattering and tetraquarks in two-dimensional QCD
• Exotic hadrons associated with $b$-quark
• Wilson loops with neural networks