Multi-quark energies in QCD

TL;DR

This paper evaluates four-quark potentials in SU(2) lattice QCD, revealing that a two-body approximation significantly overestimates binding energies for certain configurations.

Contribution

The study provides the first detailed lattice calculation of four-quark energies in SU(2) and critically assesses the validity of two-body potential models.

Findings

Two-body approach overestimates binding energy by up to a factor of three.

Four-quark potentials depend on the geometric configuration of quarks.

Results highlight limitations of simplified models in multiquark systems.

Abstract

Four-quark potentials for $SU(2)$ are evaluated in the static limit with the quenched approximation -- using a lattice of $16^3\times 32$ and $\beta=2.4$. The four quarks are restricted to the corners of rectangles with sides upto seven lattice spacings long. The results are analysed in terms of a strategy based on interquark two-body potentials -- as advocated earlier by the authors. This shows that a standard two-body approach overestimates the four-quark binding energy by upto a factor of about three for the largest rectangles.