$\Omega$-dibaryon production with hadron interaction potential from the lattice QCD in relativistic heavy-ion collisions

Recently the HAL QCD Collaboration reported the $\Omega-\Omega$ and $N-\Omega$ interaction potentials by the lattice QCD simulations. Based on these results, $N\Omega$ ($^5S_2$) and $\Omega\Omega$ ($^1S_0$) bound states were predicted with the binding energy about a few MeV. In addition, $N-\Omega$ HBT correlation function was also measured by the STAR Collaboration as well as the ALICE Collaboration. These results provide dynamical information whether or not $\Omega$-dibaryons exist in the interaction aspects. Another necessary point for the detection of $\Omega$-dibaryons is the experimental environment where the bound state could be produced and survived in the system. In this context, there are at least two necessary conditions to constrain the production probability of $\Omega$-dibaryons, i.e. the one is the necessary short-range attractive interaction to form the bound state and the another is the experimental environment such as heavy-ion collision provides abundant enough strangeness and multiplicity of nucleons. In this Letter the $\Omega-\Omega$ and $\Omega-$nucleon interaction potentials by the lattice QCD simulations were employed to obtain $\Omega\Omega$ ($^1S_0$) and $N\Omega$ ($^5S_2$) wave functions, and then the productions of $\Omega$-dibaryons were estimated by using of a dynamical coalescence mechanism for the relativistic heavy-ion collisions at $\sqrt{s_{NN}} = $ 200 GeV and 2.76 TeV.