Diffusion Monte Carlo calculations of fully-heavy (multiquark) bound states

Abstract

We use a diffusion Monte Carlo method to solve the many-body Schrödinger 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.

Comments: 19 pages, 7 figures, 15 tables