An Analysis of Four-quark Energies in SU(2) Lattice Monte Carlo using the Flux-tube Symmetry:

Abstract

Energies of four-quark systems calculated by the static quenched SU(2) lattice Monte Carlo method are analyzed in $2\times 2$ bases for square, rectangle, tilted rectangle, linear and quadrilateral geometry configurations and in $3\times 3$ bases for a non-planar geometry configuration. For small interquark distances, a lattice effect is taken into account by considering perimeter dependent terms which are characterized by the cubic symmetry. It is then found that a parameter $f$ - that can be identified as a gluon field overlap factor - is rather well described by the form $exp(-[b_{s}E\mathcal{A}+\sqrt{b_s}F\mathcal{P}])$, where $\mathcal{A}$ and $\mathcal{P}$ are the area and perimeter mainly defined by the positions of the four quarks, $b_s$ is the string constant in the 2-quark potentials and $E,F$ are constants.

Comments: (19 pages of Latex - 1 page of figures not included - sent on request). Preprint HU-TFT-94-28