Valence QCD: Connecting QCD to the quark model

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. It is shown in this valence version of QCD that the ratios of isovector to isoscalar matrix elements (e.g., ${F}_{A}{/D}_{A}$ and ${F}_{S}{/D}_{S}$ ratios) in the nucleon reproduce the SU(6) quark model predictions in a lattice QCD calculation. We also consider how the hadron masses are affected on the lattice and discover new insights into the origin of dynamical mass generation. It is found that, within statistical errors, the nucleon and the $\ensuremath{\Delta}$ become degenerate for the quark masses we have studied (ranging from 1 to 4 times the strange mass). The $\ensuremath{\pi}$ and $\ensuremath{\rho}$ become nearly degenerate in this range. It is shown that valence QCD has the C, P, T symmetries. The lattice version is reflection positive. It also has the vector and axial symmetries. The latter leads to a modified partially conserved axial Ward identity. As a result, the theory has a $\mathrm{U}{(2N}_{F})$ symmetry in the particle-antiparticle space. Through lattice simulation, it appears that this is dynamically broken down to ${\mathrm{U}}_{q}{(N}_{F})\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{\overline{q}}{(N}_{F})$. Furthermore, the lattice simulation reveals spin degeneracy in the hadron masses and various matrix elements. This leads to an approximate ${\mathrm{U}}_{q}{(2N}_{F})\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{\overline{q}}{(2N}_{F})$ symmetry which is the basis for the valence quark model. In addition, we find that the masses of N, $\ensuremath{\Delta},\ensuremath{\rho},\ensuremath{\pi}{,a}_{1}$, and ${a}_{0}$ all drop precipitously compared to their counterparts in the quenched QCD calculation. This is interpreted as due to the disappearance of the ``constituent'' quark mass which is dynamically generated through tadpole diagrams. The origin of the hyperfine splitting in the baryon is largely attributed to the Goldstone boson exchanges between the quarks. Both of these are the consequences of the lack of chiral symmetry in valence QCD. We discuss its implications concerning the models of hadrons.