Continuum extrapolation of energies of a four-quark system in lattice gauge theory

Abstract

A continuum extrapolation of static two- and four-quark energies calculated in quenched SU(2) lattice Monte Carlo is carried out based on Sommer's method of setting the scale. The beta-function is obtained as a side product of the extrapolations. Four-quark binding energies are found to be essentially constant at beta >= 2.35 unlike the two-body potentials. A model for four-quark energies, with explicit gluonic degrees of freedom removed, is fitted to these energies and the behaviour of the parameters of the model is investigated. An extension of the model using the first excited states of the two-body gluon field as additional basis states is found to be necessary for quarks at the corners of regular tetrahedra.

21 pages, 5 ps figures. Version to be published in Phys. Rev. D: Discussion of the beta function expanded and updated to three loops, section on developing the model distinguishes between two-body excitations with different symmetries

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• First Evidence of $N_f$-Dependence in the QCD Interquark Potential
• Hadronic Correlation Functions in the Interacting Instanton Liquid
• The Structure of Flux-tubes in SU(2)
• Lattice sum rules for the colour fields
• A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo
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• A variational fit to the lattice energy of two heavy-light mesons
• Four-quark flux distribution and binding in lattice SU(2)
• Dynamical effects of QCD in $q^2{\bar{q}}^2$ systems
• A model for multi-quark systems
• Glueballs and Hybrids (Gluons as Constituents)
• Four-quark systems
• ${\bar{D}}^0{D}^{0\ast }$ $(D^0{\bar{D}}^{0\ast })$ System in QCD-Improved Many Body Potential
• Flux-tube Structure, Sum Rules and Beta-functions in SU(2)