Study of degenerate four-quark states with SU(2) lattice Monte Carlo techniques

The energies of four-quark states are calculated for geometries in which the quarks are situated on the corners of a series of tetrahedra and also for geometries that correspond to gradually distorting these tetrahedra into a plane. The interest in tetrahedra arises because they are composed of three degenerate partitions of the four quarks into two two-quark color singlets. This is an extension of earlier work showing that geometries with two degenerate partitions (e.g., squares) experience a large binding energy. It is now found that even larger binding energies do not result, but that for the tetrahedra the ground and first excited states become degenerate in energy. The calculation is carried out using SU(2) for static quarks in the quenched approximation with beta = 2.4 on a 16(3) x 32 lattice. The results are analyzed using the correlation matrix between different Euclidean times and the implications of these results are discussed for a model based on two-quark potentials.