Abstract
We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for multi-particle correlations in the physical observables, and avoids the usual quark-clustering assumed in other theoretical techniques applied to the same problem. The interaction between particles was modeled by the most general and accepted potential, i.e. a pairwise interaction including Coulomb, linear-confining and hyperfine spin-spin terms. This means that, in principle, our analysis should provide some rigorous statements about the mass location of the all-heavy tetraquark ground states, which is particularly timely due to the very recent observation made by the LHCb collaboration of some enhancements in the invariant mass spectra of $J/\psi$-pairs. Our main results are: (i) the $cc\bar c\bar c$, $cc\bar b\bar b$ ($bb\bar c\bar c$) and $bb\bar b \bar b$ lowest-lying states are located well above their corresponding meson-meson thresholds; (ii) the $J^{PC}=0^{++}$ $cc\bar c\bar c$ ground state with preferred quark-antiquark pair configurations is compatible with the enhancement(s) observed by the LHCb collaboration; (iii) our results for the $cc\bar c\bar b$ and $bb\bar c\bar b$ sectors seem to indicate that the $0^+$ and $1^+$ ground states are almost degenerate with the $2^+$ located around $100\,\text{MeV}$ above them; (iv) smaller mass splittings for the $cb\bar c\bar b$ system are predicted, with absolute mass values in reasonable agreement with other theoretical works; (v) the $1^{++}$ $cb\bar c\bar b$ tetraquark ground state lies at its lowest $S$-wave meson-meson threshold and it is compatible with a molecular configuration.
Highlights
The J=ψ signal was observed simultaneously at Brookhaven [1] and SLAC [2] in 1974; it was a heavy resonance with a surprisingly small decay width
We find fully heavy tetraquark computations based on phenomenological mass formulas [34,35,36], quantum chromodynamics (QCD) sum rules [32,37,38,39], QCD-motivated bag models [40], NR effective field theories [41,42], potential models [33,43,44,45,46,47,48,49,50,51,52,53,54,55], nonperturbative functional methods [56], and even some exploratory lattice-QCD calculations [57]
The second feature, accurateness, is fulfilled using a diffusion Monte Carlo (DMC) technique for solving the many-body Schrödinger equation which, in contrast with variational methods, allows us to reduce the uncertainty of the numerical calculation at the percent level, since the systematic one associated with the trial wave function is eliminated by the algorithm
Summary
The J=ψ signal was observed simultaneously at Brookhaven [1] and SLAC [2] in 1974; it was a heavy resonance with a surprisingly small decay width. An even heavier resonance but narrow, the so-called Υ state, was observed at Fermilab [3,4]. The interpretation of the J=ψ and Υ as low-lying bound states of a heavy quark, Q, and its antiquark, Q , with Q either a c or b quark, explained their narrow decay widths and, was proved to be crucial to establishing quantum chromodynamics (QCD) as the strong-interaction sector of the Standard Model of particle physics [5,6]. It is worth mentioning that a related system, the cbbound state ðBþc Þ, has been found in nature [7]; and that the heaviest of the quarks—i.e., the top quark—was discovered in 1995 at Fermilab [8], with a mass around 175 GeV and a large
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