Most Strange Dibaryon from Lattice QCD

The $\mathrm{\Omega }\mathrm{\Omega }$ system in the ${}^1{S}_0$ channel (the most strange dibaryon) is studied on the basis of the ($2+1$)-flavor lattice QCD simulations with a large volume $(8.1\mathrm{fm}{)}^3$ and nearly physical pion mass $m_{\pi }\simeq 146\mathrm{MeV}$ at a lattice spacing of $a\simeq 0.0846\mathrm{fm}$. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length $a_0=4.6(6){(}_{-0.5}^{+1.2})\mathrm{fm}$, the effective range $r_{\mathrm{eff}}=1.27(3){(}_{-0.03}^{+0.06})\mathrm{fm}$, and the binding energy $B_{\mathrm{\Omega }\mathrm{\Omega }}=1.6(6){(}_{-0.6}^{+0.7})\mathrm{MeV}$. These results indicate that the $\mathrm{\Omega }\mathrm{\Omega }$ system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions.

Figure 1

The $\mathrm{\Omega }\mathrm{\Omega }$ potential $V(r)$ in the ${}^1{S}_0$ channel at Euclidean time $t/a=16$, 17, and 18.

Figure 2

The $\mathrm{\Omega }\mathrm{\Omega }$ phase shift $\delta (k)$ in the ${}^1{S}_0$ channel for $t/a=16$, 17, and 18 as a function of the center of mass kinetic energy $E_{\mathrm{CM}}=2\sqrt{k^2+m_{\mathrm{\Omega }}^2}-2m_{\mathrm{\Omega }}$.

Figure 3

The dimensionless ratio of the effective range $r_{\mathrm{eff}}$ and the scattering length $a_0$ as a function of $r_{\mathrm{eff}}$ for the $\mathrm{\Omega }\mathrm{\Omega }$ system in the ${}^1{S}_0$ channel as well as for the spin-triplet $NN$ system (the deuteron channel) and for the spin-singlet $NN$ system (the neutron-neutron channel). The error bar for $\mathrm{\Omega }\mathrm{\Omega }$ is the quadrature of the statistical and systematic errors in Eqs. (7) and (8).

Figure 4

Bound state energy of the $\mathrm{\Omega }\mathrm{\Omega }$ system and the root-mean-square distance between $\mathrm{\Omega }$’s obtained from the potential. The filled diamond (triangle) corresponds to the result at $t/a=17$ without (with) the Coulomb repulsion. The statistical errors are shown by the solid lines, while the systematic errors estimated from the difference between the data at $t/a=17$ and those at $t/a=16$, 18 are shown by the dashed lines.