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We use a diffusion Monte Carlo method to solve the many-body Schr\"odingerequation describing fully-heavy tetraquark systems. This approach allows toreduce the uncertainty of the numerical calculation at the percent level,accounts for multi-particle correlations in the physical observables, andavoids the usual quark-clustering assumed in other theoretical techniquesapplied to the same problem. The interaction between particles was modeled bythe most general and accepted potential, i.e. a pairwise interaction includingCoulomb, linear-confining and hyperfine spin-spin terms. This means that, inprinciple, our analysis should provide some rigorous statements about the masslocation of the all-heavy tetraquark ground states, which is particularlytimely due to the very recent observation made by the LHCb collaboration ofsome enhancements in the invariant mass spectra of $J/\psi$-pairs. Our mainresults 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 theircorresponding meson-meson thresholds; (ii) the $J^{PC}=0^{++}$ $cc\bar c\bar c$ground state with preferred quark-antiquark pair configurations is compatiblewith the enhancement(s) observed by the LHCb collaboration; (iii) our resultsfor 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 $2^+$ locatedaround $100\,\text{MeV}$ above them; (iv) smaller mass splittings for the$cb\bar c\bar b$ system are predicted, with absolute mass values in reasonableagreement with other theoretical works; (v) the $1^{++}$ $cb\bar c\bar b$tetraquark ground state lies at its lowest $S$-wave meson-meson threshold andit is compatible with a molecular configuration.

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