ar X iv : h ep - l at / 9 41 20 29 v 1 5 D ec 1 99 4 Four - quark energies in SU ( 2 ) lattice Monte Carlo using a tetrahedral geometry ∗

This contribution – a continuation of the work in refs.[1]-[4] – reports on recent developments in the calculation and understanding of 4-quark energies generated using lattice Monte Carlo techniques. In refs.[3,4] – the binding energies of four quarks in various geometries (e.g. at the corners of a rectangle or on a straight line) were calculated in static-quenched-SU(2) on a lattice 16 3 × 32 with β = 2.4. This showed that the 4-quark binding energies were greatest when two of the three possible partitions of the four quarks – into two colour-singlet pairs – were degenerate in energy e.g. as in a square geometry. The main reasons for studying other geometries were: 1) to investigate further this point and 2) to give a representative set of geometries illustrating the different possibilities for arranging four quarks. The latter would then serve as a very stringent test of models attempting to describe four interacting quarks – provided such models involve approximations analogous to those contained in the corresponding lattice calculation e.g. static quarks and SU(2). Interest in the tetrahedral geometry arises, since in this case all three partitions are degen-* This work is part of the EC Programme " Human Capital and Mobility " – project number ERB-CHRX-CT92-0051 – and was presented by A.M.Green. are now studied. Preliminary results are given in table 1. Table 1 The ground and first excited state energies (E 0,1). The results for r = 0 are from ref.[4] for the 1 × 1-square using 2 partitions and those for r = d for the Tetrahedron. All energies are given in terms of lattice units at β = 2.4, which corresponds to an inverse lattice spacing a