Study of Quark Confinement in Baryons with Lattice QCD

In SU(3) lattice QCD, we perform the detailed study for the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, i.e., the energies of the ground state and the 1st excited state of the gluon field in the presence of the static three quarks. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ 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 calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model even without gluonic excitations. We present also the first study for the penta-quark potential $V_{\rm 5Q}$ in lattice QCD, and find that $V_{\rm 5Q}$ is well described by the sum of the OGE Coulomb plus multi-Y type linear potential.