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

TL;DR

This paper analyzes four-quark energies in SU(2) lattice Monte Carlo simulations, revealing how a gluon field overlap factor depends on geometric parameters like area and perimeter, with implications for understanding multi-quark systems.

Contribution

It introduces a model describing the gluon field overlap factor in four-quark systems using geometric parameters, extending previous lattice QCD analyses.

Findings

The gluon overlap factor f fits an exponential form involving area and perimeter.

Perimeter-dependent lattice effects are significant at small interquark distances.

The model successfully describes energy dependencies in various geometric configurations.

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 $exp(-[b_sE{\cal A}+\sqrt{b_s}F{\cal P}])$, where ${\cal A}$ and ${\cal P}$ 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.