  We present results of the first lattice QCD calculation of three-flavored
heavy dibaryons both in the flavor-symmetric and antisymmetric channels. These
dibaryons have spin zero, and are constructed using various possible
combinations of quark flavors with at least one of them as the charm or the
bottom quark, i.e., namely, $H_c(cudcud), H_b(budbud), H_{bcs}(bcsbcs)$,
$H_{csl}(cslcsl), H_{bsl}(bslbsl)$ and $H_{bcl}(bclbcl)$; $l\in u,d$. We
compute the ground state masses of these dibaryons and the calculations are
performed on three $N_f=2+1+1$ HISQ gauge ensembles of the MILC collaboration,
with lattice spacings $a =$ 0.1207, 0.0888 and 0.0582 fm. A relativistic
overlap action is employed for the valence light to charm quarks while a
non-relativistic-QCD Hamiltonian with improved coefficients is used for the
bottom quarks. Unlike the doubly heavy tetraquarks, one and two-flavored heavy
dibaryons, for which lattice QCD calculations have predicted deeply bound
strong-interactions-stable states, for these $H_c, H_b, H_{csl},H_{bsl}$
dibaryons we do not find any such deeply bound state. However, for $H_{bcs}$,
our results indicate the presence of an energy level $29\pm 24$ MeV below the
lowest two-baryon threshold, which could be relevant for its future
experimental searches. Moreover, we find that the energy difference between the
ground state of $H_{bcl}$ and its lowest threshold increases when $m_l>m_s$.
Taken together, our findings indicate the possibility of the existence of the
$H_{bcs}$ dibaryon while all other physical three-flavored dibaryons are much
closer to their thresholds suggesting either they are weakly bound or unbound,
resolving which requires further detail study. Our results also point that the
binding of a dibaryon configuration becomes stronger with the increase of its
valence quark masses which suggests an interesting aspect of strong
interactions at multiple scales.
