A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

TL;DR

This study investigates four-quark states in SU(2) lattice QCD, revealing degeneracy in ground and excited states for tetrahedral geometries, and analyzes their energies using correlation matrices in a quenched approximation.

Contribution

It extends previous work by exploring tetrahedral four-quark configurations and their energy degeneracies using lattice Monte Carlo simulations.

Findings

Degeneracy of ground and first excited states in tetrahedral geometries.

No larger binding energies observed for tetrahedra compared to other geometries.

Implications for two-quark potential models discussed.

Abstract

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 {\bf three } degenerate partitions of the four quarks into two two-quark colour singlets. This is an extension of earlier work showing that geometries with {\bf 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 $16^3\times 32$ lattice. The results are analysed using the correlation matrix between different euclidean times and the implications of these results are discussed for a model based on two-quark potentials.