ar X iv : h ep - l at / 9 90 80 32 v 1 2 2 A ug 1 99 9 1 NORDITA - 1999 / 50 HE Interactions of heavy - light mesons ∗

The potential between static-light mesons forming a meson-meson or a meson-antimeson system is calculated in quenched and unquenched SU(3) gauge theory. We use the Sheikholeslami-Wohlert action and statistical estimators of light quark propagators with maximal variance reduction. The dependence of the potentials on the light quark spin and isospin and the effect of meson exchange is investigated. Our main motivation is exploration of bound states of two mesons and string breaking. The latter also involves the two-quark potential and the correlation between two-quark and two-meson states. We have been working on lattice calculations of multiquark systems in order to understand their properties from first principles. Here " multi " means that the system can be decomposed into more than one colour singlet, the simplest case being four quarks. Previously, we have studied four quarks in the static approximation in SU(2), getting energies for a general set of geometries which have been reproduced by a model based on two-body potentials and multiquark interaction terms [1]. We have also looked at the flux distribution corresponding to the binding energy [2]. These results for the static case are discussed in last year's proceedings. In the current work only two of the quarks are static and SU(3) is used, also unquenched. The binding of this system of two heavy-light mesons is studied as a function of the heavy quark separation. Different cases of spin and isospin of the light quarks are measured and the effect from meson exchange is extracted from the potentials. The model for energies of static quarks is extended for this more dynamic system as discussed in Ref. [3] and by A.M. Green in these proceedings. The meson-antimeson case with light quark isospin I q = 0 is relevant to string breaking. In the future we plan to explore breaking of an excited string, which is interesting from the point of view of hybrid meson phenomenlogy. 1. TWO HEAVY-LIGHT MESONS Experimental candidates for bound states of four quarks (of which two are antiquarks) lie close to meson-antimeson thresholds. In our case e.g. a heavy Υ particle could be a B * ¯ B * system. Systems with heavy quarks should be more easily bound as the repulsive kinetic energy is smaller with the attractive potential being flavour independent. The binding of four-quark systems has been studied e.g. in bag, string-flip and deuson models, states with two b quarks being stable in …