Y-type Flux-Tube Formation in Baryons

Abstract

For more than 300 different patterns of the 3Q systems, the ground-state 3Q potential $V_{3Q}^{g.s.}$ 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 $V_{3Q}^{g.s.}$ is well described with so-called Y-ansatz as $V_{3Q}=-A_{3Q}{\sum }_{i<j}\frac{1}{|{\mathbf{r}}_i-{\mathbf{r}}_j|}+{\sigma }_{3Q}{L}_{\min }+C_{3Q}$, with the accuracy better than 1%. Here, $L_{\min }$ denotes the minimal value of total flux-tube length. We also studythe excited-state potential $V_{3Q}^{e.s.}$ 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 $V_{3Q}^{g.s.}$ and $V_{3Q}^{e.s.}$, 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.

Comments: Talk given at Color Confinement and Hadrons in Quantum Chromodynamics (Confinement 2003), Saitama, Japan, 21-24 July 2003; 5 pages, 4 figures