Lattice QCD study of baryon-baryon interactions in the (S,I)=(-2,0) system using the coupled-channel formalism

TL;DR

This study uses Lattice QCD to analyze baryon-baryon interactions with strangeness -2 and isospin 0, employing a coupled-channel formalism to compute the potential matrix and explore SU(3) flavor symmetry breaking effects.

Contribution

It introduces a coupled-channel Lattice QCD method to calculate baryon-baryon potentials in the (S,I)=(-2,0) system, including SU(3) breaking effects, using a 3x3 correlation matrix approach.

Findings

Calculated the 3x3 potential matrix for the system.

Analyzed SU(3) flavor symmetry breaking effects.

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.