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-type underestimating binding energies.
Including heavy spin effects in the prediction of a $\bar{b} \bar{b} u d$ tetraquark with lattice QCD potentials
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abstract
We investigate spin effects in four-quark systems consisting of two heavy anti-bottom quarks and two light up/down quarks. To this end we use the Born-Oppenheimer approximation. We utilize potentials of two static antiquarks in the presence of two quarks of finite mass computed via lattice QCD and solve a coupled-channel Schr\"odinger equation for the anti-bottom-anti-bottom separation. Without taking heavy quark spins into account this approach predicted a $u d \bar b \bar b$ tetraquark bound state with quantum numbers $I(J^P) = 0(1^+)$. We now extend this Born-Oppenheimer approach with coupled channel Schr\"odinger equations allowing us to incorporate effects due to the heavy $\bar b$ spins. We confirm the existence of the $u d \bar b \bar b$ tetraquark.
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2026 1verdicts
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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-type underestimating binding energies.