Four-quark Systems *

In order to understand the binding of four static quarks, flux distributions corresponding to these binding energies are studied in quenched SU(2) and also related to a model for the energies. The potential relevant to string breaking between two heavy-light mesons is measured in quenched SU(3) using stochastic estimates of light quark propagators with the Sheikholeslami-Wohlert action. Our goal is to understand multi-quark interactions from first principles. Since " multi-quark " means that the system can be decomposed into more than one color singlet, the simplest such system consists of four quarks. In this work we try to understand this simple case, relevant for meson-meson interactions, hoping that generalization to more complicated cases will be relatively straightforward. We first give a brief introduction to a model that reproduces one hundred ground-and excited state energies of four static quarks [1]. These energies have been calculated earlier in SU(2) gauge theory on ≈ 20 3 × 32 lattices with a ≈ 0.1 fm – a continuum extrapolation has been performed [2]. The flux distribution producing four-quark binding has been measured [3] and we attempt to relate it to our model. Preliminary results are reported from a more realistic calculation concerning the potential between two heavy-light mesons in quenched SU(3). The heavy quarks are taken to be static and the light quark propagators are calculated using stochastic estimators with an O(a) improved fermion action. This work also concerns string breaking. 1. The model We like to think of the simplest multi-quark system, consisting of four quarks, as a bridge between a single hadron and interacting multi-hadron systems. Earlier, simulations of static four-quark systems have been performed for a general set of geometries [2,4, references therein]. These quenched SU(2) calculations have produced binding energies up to 120 MeV. In order to understand these results a phenomenological model based on two-body potentials and multi-quark interaction terms has been developed. The basis states of the model come from the three possible ways to pair four quarks into two mesons in SU(2). These pairing are taken to be in the ground state (A, B, C) or first excited state (A * , B * , C *) of the two-body potential, giving six states (A,. .. , C *) in total. The basic equation of the model is