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One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
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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 Schr\"odinger 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.
Forward citations
Cited by 9 Pith papers
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Open-flavor threshold effects on quarkonium spectrum in the BOEFT
BOEFT quantifies threshold-induced shifts in quarkonium masses below threshold by solving coupled Schrödinger equations using lattice potentials and one parameter fixed to the χ_c1(3872) mass.
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Neural network interpolators for Wilson loops
Neural networks parametrize gauge-equivariant trial states for Wilson loops and automatically yield interpolators for ground and excited states in quenched lattice QCD.
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Wilson loops with neural networks
Neural networks parametrize gauge-invariant interpolators that extract ground-state Wilson loops with improved signal-to-noise ratio compared to traditional methods while preserving gauge invariance.
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Hybrid hadrons at rest and on the light front
A constituent-gluon Born-Oppenheimer model is used to derive light-front wave functions and gluon PDFs for hybrid hadrons ccg and qqqg.
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$\boldsymbol{\chi_{c1}}(3872)$ and its Partners in the Diabatic Born-Oppenheimer Approximation for QCD
χ_c1(3872) is treated as a bound state in adjoint-meson Born-Oppenheimer potentials within a diabatic model, with calculated spin splittings and decay widths for its multiplet and bottom analogs after tuning to threshold.
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A New Look at the X Compositeness from its Lineshape
An auxiliary-field effective theory yields a lineshape parametrization for molecular X(3872) that consistently describes deuteron scattering data and differs from the Flatté form used for compact interpretations.
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Hybrid hadrons at rest and on the light front
Derives light-front wave functions for ccg and qqqg hybrid hadrons via variational and numerical Schrödinger methods in a constituent-gluon Born-Oppenheimer picture and computes the resulting gluon PDFs.
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Assessing the validity of the Born-Oppenheimer approximation in potential models for doubly heavy hadrons
Born-Oppenheimer approximation calculations for doubly heavy hadrons match Gaussian expansion benchmarks at small heavy quark masses but diverge at larger masses, with Slater-type functions overestimating and Gaussian...
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$\lambda$, $\rho$, and $\sigma$ Regge trajectories for the quadruply heavy pentaquark $bb\bar{u}cc$ in the diquark-triquark picture
Regge relations for bbūcc in the diquark-triquark picture give four trajectory series with M∼x^{2/3} or √x behavior plus spin-averaged mass estimates for λ, ρ1, ρ2 and σ excitations.
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