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

A continuum extrapolation of static two- and four-quark energies calculated in a quenched SU(2) lattice Monte Carlo simulation 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 behavior 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.