Color SU(3) symmetry, confinement, stability, clustering and quark mass dependence in theq4q¯system

Abstract

We examine the color SU(3) dynamics of q{sup 4}q 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.