Multi-Quark Energies in SU(2) Lattice Gauge Theory

TL;DR

This study computes four-quark energies in SU(2) lattice gauge theory using Monte Carlo simulations, analyzing different geometries and lattice parameters to understand interquark interactions and gluon-field effects.

Contribution

It provides new lattice calculations of four-quark energies in SU(2), exploring geometric configurations and scaling effects, and introduces a phenomenological model incorporating gluon-field overlaps.

Findings

Four-quark energies depend on geometry and lattice size.

Finite size and scaling effects are quantitatively analyzed.

A modified interquark potential model with gluon-field overlap is proposed.

Abstract

Energies of four-quark systems have been extracted in a quenched SU(2) lattice Monte Carlo calculation for two different geometries, rectangular and colinear, with $\beta=2.4$ and lattice size $16^3\times 32$. Also, by going to a lattice $24^3\times 32$ and to $\beta=2.5$, the effect of the finite lattice size and scaling are checked. An attempt is made to understand these results in terms of a model based on interquark two-body potentials but modified very significantly by a phenomenological gluon-field overlap factor.