$\Omega \Omega$ interaction from 2+1 flavor lattice QCD

Abstract

We investigate the interaction between $\Omega$ baryons in the ${}^1{S}_0$ channel from 2+1 flavor lattice QCD simulations. On the basis of the HAL QCD method, the $\Omega \Omega$ potential is extracted from the Nambu-Bethe-Salpeter wave function calculated on the lattice by using the PACS-CS gauge configurations with the lattice spacing $a\simeq 0.09$ fm, the lattice volume $L\simeq 2.9$ fm and the quark masses corresponding to $m_{\pi }\simeq 700$ MeV and $m_{\Omega }\simeq 1970$ MeV. The $\Omega \Omega$ potential has a repulsive core at short distance and an attractive well at intermediate distance. Accordingly, the phase shift obtained from the potential shows moderate attraction at low energies. Our data indicate that the $\Omega \Omega$ system with the present quark masses may appear close to the unitary limit where the scattering length diverges.

Comments: 9 pages, 4 figures, 1 table