Interaction between two heavy mesons in QCD 2

Abstract

The interaction between two heavy mesons each consisting of a light quark and a heavy antiquark in two-dimensional QCD (QCD 2) is studied in the large- N (number of colors) limit. The ordinary coordinate formulation of Bars and Green is used to construct the vacuum and the light-meson states. The heavy-meson problem is then solved in the limit of infinite antiquark mass. The energy of a two-heavy-meson system is then calculated by examining the role of light antiquarks. The only role of the light antiquarks is found to give rise to the light-meson-exchange potential. The remaining interactions are caused by the exchange of light quarks within the framework of the ordinary quantum mechanics. This can therefore be considered as a concrete example of the hybrid model for hadron-hadron interactions where the quark-exchange and the meson-exchange contributions are unified in a natural way. The similarities of each contribution to that in the models of the real world are discussed. Many features are found to be common for two and four dimensions and thus the hadronic interaction in QCD 2 is worth studying in getting insights to those in QCD 4. We show that these potentials are similar to what have been observed in the quark model calculations in four dimensions.