Y-type Flux-Tube Formation in Baryons

Abstract

For more than 300 different patterns of the 3Q systems, the ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated using SU(3) lattice QCD with $12^3\times 24$ at $\beta=5.7$ and $16^3\times 32$ at $\beta=5.8, 6.0$ at the quenched level. As a result of the detailed analyses, we find that the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is well described with so-called Y-ansatz as $V_{\rm 3Q}=-A_{\rm 3Q}\sum_{i<j}\frac1{|{\bf r}_i-{\bf r}_j|} +\sigma_{\rm 3Q} L_{\rm min}+C_{\rm 3Q}$, with the accuracy better than 1%. Here, $L_{\rm min}$ denotes the minimal value of total flux-tube length. We also studythe excited-state potential $V_{\rm 3Q}^{\rm e.s.}$ using lattice QCD with $16^3\times 32$ at $\beta=5.8, 6.0$ for more than 100 patterns of the 3Q systems. The energy gap between $V_{\rm 3Q}^{\rm g.s.}$ and $V_{\rm 3Q}^{\rm e.s.}$, which physically means the gluonic excitation energy, is found to be about 1 GeV in the typical hadronic scale. Finally, we suggest a possible scenario which connects the success of the quark model to QCD.