Strongly Bound Dibaryon with Maximal Beauty Flavor from Lattice QCD

We report the first lattice QCD study of the heavy dibaryons in which all six quarks have the bottom (beauty) flavor. Performing a state-of-the-art lattice QCD calculation we find clear evidence for a deeply bound ${\mathrm{\Omega }}_{bbb}\text{−}{\mathrm{\Omega }}_{bbb}$ dibaryon in the ${}^1{S}_0$ channel, as a pole singularity in the $S$-wave ${\mathrm{\Omega }}_{bbb}\text{−}{\mathrm{\Omega }}_{bbb}$ scattering amplitude with a binding energy $-81({}_{-16}^{+14})\mathrm{MeV}$. With such a deep binding, Coulomb repulsion serves only as a perturbation on the ground state wave function of the parametrized strong potential and may shift the strong binding only by a few percent. Considering the scalar channel to be the most bound for single flavored dibaryons, we conclude this state is the heaviest possible most deeply bound dibaryon in the visible universe.

Figure 1

Lattice QCD ensembles, with sizes $N_s^3\times N_t$, used in this work. Here, $L=N_{s}a$ is the spatial extent of the lattice.

Figure 2

Effective masses corresponding to the ground states of the noninteracting two-baryon and dibaryon correlators on the finest lattice ensemble determined from wall-to-point correlation functions. An energy gap between them is clearly visible at all time slices. The solid bands show the fit estimates and fit windows.

Figure 3

Results from the finite-volume scattering analysis. Top: Comparison of the simulated energy levels (large symbols) with the energy levels (black stars) analytically reconstructed using Eq. (7), indicating the quality of the scattering analysis fit. Middle: $k\cot {\delta }_0$ versus $k^2$ in units of energy of the threshold ($2M_{{\mathrm{\Omega }}_{bbb}}$) and information on poles in $t$ indicated by magenta symbols. Bottom: Continuum extrapolation of the binding energy in Eq. (8) determined from fitted scattering amplitude in Eq. (7).

Figure 4

Coulomb ($V_e$), the parametrized strong potentials ($V_s$) and their sum are shown by the black, blue, and red curves, respectively. The shaded region represents the variation of $V_s$ with respect to its parameters. $V_e$ is evaluated at a rms charge radius equal to the rms radius of the $V_s$ ground state. The radial probability densities of the ground state wave functions of the strong and combined potentials are shown by the dashed-dotted curves.