Three Baryon Interaction Generated by Determinant Interaction of Quarks

We discuss the three-baryon interaction generated by the determinant interaction of quarks, known as the Kobayashi-Maskawa-'t Hooft (KMT) interaction. The expectation value of the KMT interaction operator is calculated in fully-antisymmetrized quark-cluster model wave functions for one-, two- and three-octet baryon states. The three-baryon potential from the KMT interaction is found to be repulsive for $NN\mathrm{\Lambda }$ and $N\mathrm{\Lambda }\mathrm{\Lambda }$ systems, while it is zero for the $NNN$ system. The strength and range of the three-baryon potential are found to be comparable to those for the $NNN$ three-body potential obtained in lattice QCD simulations. The contribution to the $\mathrm{\Lambda }$ single particle potential in nuclear matter is found to be 0.28 MeV and 0.73 MeV in neutron matter and symmetric nuclear matter at normal nuclear density, respectively. These repulsive forces are not enough to solve the hyperon puzzle, but may be measured in high-precision hyperisotope experiments.