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

TL;DR

This study uses lattice QCD to analyze baryon-baryon interactions with strangeness -2 and isospin 0, constructing coupled-channel potentials and examining SU(3) flavor symmetry breaking effects.

Contribution

It introduces a coupled-channel approach to compute baryon-baryon potentials from lattice QCD, including SU(3) breaking effects, for the first time in this context.

Findings

Calculated the 3x3 potential matrix for S=-2, I=0 baryon interactions.

Demonstrated flavor SU(3) breaking effects on the potential matrix.

Provided numerical results from 2+1 flavor QCD configurations.

Abstract

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.