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 16 × 32 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 V e.s. 3Q together with the ground-state potential V g.s. 3Q by diagonalizing the QCD Hamiltonian in the presence of three quarks. The gluonic excitation energy ∆E3Q ≡ V e.s. 3Q − V g.s. 3Q 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 ∆E3Q in terms of the 3Q location. The lattice data of ∆E3Q 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.