Coupled channel approach to (S,I)=(-2,0) baryon-baryon interactions from lattice QCD

We investigate baryon-baryon interactions with strangeness $S=-2$ and isospin I=0 system from Lattice QCD. In order to solve this system, we prepare three types of baryon-baryon operators ($\Lambda\Lambda$, $N\Xi$ and $\Sigma\Sigma$) for the sink and construct three source operators diagonalizing the $3\times3$ correlation matrix. Combining of the prepared sink operators with the diagonalized source operators, we obtain nine effective Nambu-Bethe-Salpeter (NBS) wave functions. The $3\times3$ potential matrix is calculated by solving the coupled-channel Schr\"odinger equation. The flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with the results of the SU(3) limit calculation. Our numerical results are obtained from three sets of 2+1 flavor QCD gauge configurations provided by the CP-PACS/JLQCD Collaborations.