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

Abstract

We study the excited-state potential and the gluonic excitation in the static three-quark (3Q) system using SU(3) lattice QCD with $16^3\times 32$ 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 $V_{\rm 3Q}^{\rm e.s.}$ together with the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three quarks. The gluonic excitation energy $ΔE_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ 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 $ΔE_{\rm 3Q}$ in terms of the 3Q location. The lattice data of $ΔE_{\rm 3Q}$ 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.