Lattice Qcd Study for the Interquark Force in Three-quark and Multi-quark Systems

We study the three-quark and multi-quark potentials in SU(3) lattice QCD. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential V g.s. 3Q is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation for the 1st excited-state 3Q potential V e.s. 3Q by diagonalizing the QCD Hamiltonian in the presence of three quarks, and find a large gluonic-excitation energy ∆E3Q ≡ V e.s. 3Q −V g.s. 3Q of about 1 GeV, which gives a physical reason of the success of the quark model. ∆E3Q is found to be reproduced by the “inverse Mercedes Ansatz”, which indicates a complicated bulk excitation for the gluonic-excitation mode. We study also the tetra-quark and the penta-quark potentials in lattice QCD, and find that they are well described by the OGE Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks. Finally, the narrow decay width of penta-quark baryons is discussed in terms of the QCD string theory.