Deuteronlike Heavy Dibaryons from Lattice Quantum Chromodynamics

We report the first lattice quantum chromodynamics (QCD) study of deuteronlike ($np$-like) dibaryons with heavy quark flavors. These include particles with the following dibaryon structures and valence quark contents: ${\mathrm{\Sigma }}_c{\mathrm{\Xi }}_{cc}(uucucc)$, ${\mathrm{\Omega }}_c{\mathrm{\Omega }}_{cc}(sscscc)$, ${\mathrm{\Sigma }}_b{\mathrm{\Xi }}_{bb}(uububb)$, ${\mathrm{\Omega }}_b{\mathrm{\Omega }}_{bb}(ssbsbb)$, and ${\mathrm{\Omega }}_{ccb}{\mathrm{\Omega }}_{cbb}(ccbcbb)$, and with spin ($J$) parity ($P$), $J^P\equiv 1^{+}$. Using a state-of-the art lattice QCD calculation, after controlling relevant systematic errors, we unambiguously find that the ground state masses of dibaryons ${\mathrm{\Omega }}_c{\mathrm{\Omega }}_{cc}(sscscc)$, ${\mathrm{\Omega }}_b{\mathrm{\Omega }}_{bb}(ssbsbb)$, and ${\mathrm{\Omega }}_{ccb}{\mathrm{\Omega }}_{cbb}(ccbcbb)$ are below their respective two-baryon thresholds, suggesting the presence of bound states that are stable under strong and electromagnetic interactions. We also predict their masses precisely. For dibaryons ${\mathrm{\Sigma }}_c{\mathrm{\Xi }}_{cc}(uucucc)$, and ${\mathrm{\Sigma }}_b{\mathrm{\Xi }}_{bb}(uububb)$, we could not reach to a definitive conclusion about the presence of any bound state due to large systematics associated with these states. We also find that the binding of these dibaryons becomes stronger as they become heavier in mass. This study also opens up the possibility of the existence of many other exotic nuclei, which can be formed through the fusion of heavy baryons, similar to the formation of nuclei of elements in the periodic table.

Figure 1

Mass differences between various spin-1 heavy dibaryons (${\mathcal{D}}_{q_1{q}_2}$) from their two-baryon threshold states. Red points represent mass differences when the threshold states are with spin-$1/2$ baryons and the green points are the same with spin-$3/2$ baryons. Results are shown at three lattice spacings and at the continuum limit with shaded bands as one sigma error.

Figure 2

Relative energy levels of the spin-1 dibaryons and their respective two-baryon noninteracting strong-decay threshold states. The horizontal line is for the closest threshold (normalized to zero) while $1/2$ and $3/2$ signify the spin of the constituent single baryons of the two-baryon threshold.

Figure 3

Binding energy of the spin-1 dibaryon ${\mathcal{D}}_{bq}$ where we kept the bottom quark fixed and vary the other quark $q$ from light to bottom quarks. Along the $x$ axis we show the ratio of the pseudoscalar mass at $m_q$ ($m_{{\pi }_q}$) to that at the bottom quark ($m_{{\eta }_b}$). As the mass of the quark $q$ increases ($m_q=m_u$ to $m_b$), the dibaryon binding energy also increases.