Color SU(3) symmetry, confinement, stability, clustering and quark mass dependence in the q4q system

We examine the color SU(3) dynamics of q4q system, i.e. of the pentaquark. First we study this system in the model with two-body interaction proportional to the color charges. We construct the potential matrix and show, (1) Confinement: the color singlet qq potential energy rises infinitely with the separation distance, (2) Stability: All colorless states' energies are bounded from below (3) Color singlet clustering: the pentaquark color-singlet state Hamiltonian turns into a sum of a three-quark (baryon) and a quark-antiquark (meson) cluster Hamiltonian, in the limit of asymptotically large separations. We evaluate the four excitation eigenfrequencies of pentaquarks in the harmonic oscillator two-body confining potential and the ground states' dependence on the quark-antiquark mass ratio. We show that the pentaquark is unlikely to bind even with a top antiquark, in contrast to tetraquarks