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.

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

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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