Valence QCD: Connecting QCD to the Quark Model

Abstract

A valence QCD theory is developed to study the valence quark properties of hadrons. To keep only the valence degrees of freedom, the pair creation through the Z graphs is deleted in the connected insertions; whereas, the sea quarks are eliminated in the disconnected insertions. This is achieved with a new ``valence QCD'' lagrangian where the action in the time direction is modified so that the particle and antiparticle decouple. The theory has the vector and axial $U(2N_F)$ symmetry in the particle-antiparticle space. Through lattice simulation, it appears that this is dynamically broken down to $U_q(N_F) \times U_{\bar{q}}(N_F)$. Furthermore, the lattice simulation reveals spin degeneracy in the hadron masses and SU(6) relations in the ratios of $F_A/D_A, F_S/D_S$, and $\mu^n/\mu^p$. This leads to an approximate $U_q(2N_F) \times U_{\bar{q}}(2N_F)$ symmetry which is the basis for the valence quark model. We find that the masses of N, $\Delta, \rho, \pi, a_1$, and $a_0$ all drop precipitously compared to their counterparts in the quenched QCD calculation. This is interpreted as due to the disapperance of the `constituent' quark mass which is dynamically generated through tadpole diagrams. Form the near degeneracy between N and $\Delta$ for the quark masses we have studied (ranging from one to four times the strange mass), we conclude that the origin of the hyper-fine splitting in the baryon is largely attibuted to the Goldstone boson exchanges between the quarks. These are the consequences of lacking chiral symmetry in valence QCD. We discuss its implication on the models of hadrons.