Short-range baryon-baryon potentials in constituent quark model revisited

Abstract

We revisit the short-range baryon-baryon potentials in the flavor SU(3) sector, using the constituent quark model. We employ the color Coulomb, linear confining, and color magnetic forces between two constituent quarks, and solve the three-quark Schr\"{o}dinger equation using the Gaussian expansion method to evaluate the wave functions of the octet $( N , \Lambda , \Sigma , \Xi )$ and decuplet $( \Delta , \Sigma ^{\ast} , \Xi ^{\ast} , \Omega )$ baryons. We then solve the six-quark equation using the resonating group method and systematically calculate equivalent local potentials for the $S$-wave two-baryon systems which reproduce the relative wave functions of two baryons in the resonating group method. As a result, we find that the flavor antidecuplet states with total spin $J = 3$, namely, $\Delta \Delta$, $\Delta \Sigma ^{\ast}$, $\Delta \Xi ^{\ast}$-$\Sigma ^{\ast} \Sigma ^{\ast}$, and $\Delta \Omega$-$\Sigma ^{\ast} \Xi ^{\ast}$ systems, have attractive potentials sufficient to generate dibaryon bound states as hadronic molecules. In addition, the $N \Omega$ system with $J = 2$ in coupled channels has a strong attraction and forms a bound state. We also make a comparison with the baryon-baryon potentials from lattice QCD simulations and try to understand the behavior of the potentials from lattice QCD simulations.