Detailed analysis of the gluonic excitation in the three-quark system in lattice QCD

We study the excited-state potential and the gluonic excitation in the static three-quark (3Q) system using SU(3) lattice QCD with 163x32 at β=5.8 and 6.0 at the quenched level. For about 100 different patterns of spatially-fixed 3Q systems, we accurately extract the excited-state potential V3Qe.s. together with the ground-state potential V3Qg.s. by diagonalizing the QCD Hamiltonian in the presence of three quarks. The gluonic excitation energy ΔE3Q≡V3Qe.s.-V3Qg.s. is found to be about 1 GeV at the typical hadronic scale. This large gluonic excitation energy is conjectured to give a physical reason of the success of the quark model for low-lying hadrons even without explicit gluonic modes. We investigate the functional form of ΔE3Q in terms of the 3Q location. The lattice data of ΔE3Q are relatively well reproduced by the 'inverse Mercedes Ansatz' with the 'modified Y-type flux-tube length', which indicates that the gluonic excitation mode is realized as a complicated bulk excitation of the whole 3Q system