Y-type Flux-Tube Formation and Gluonic Excitations in Baryons: From QCD to Quark Model

Abstract

Using SU(3) lattice QCD, we perform the first systematic study for the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, {\it 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 and thorough 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, {\it i.e.}, 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 more than 100 patterns of 3Q systems, we calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ in quenched lattice QCD, and find the gluonic excitation energy $ΔE_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ to be about 1 GeV. This large gluonic-excitation energy is conjectured to ensure the success of the quark model for the low-lying hadrons even without gluonic excitations.