Quark Mass Thresholds in Quarkonium Systems

Abstract

We consider the role of quark mass thresholds in quarkonium systems, which are formed by the binding of heavy quark-antiquark pairs and are manifest in the IfJ and Y families of mesons. Such systems provide a probe of the interactions of quarks in a region accessible to the predictions of perturbative quantum chromodynamics (QCD), as well as in the long range region where the interaction is expected to show confining behaviour consistent with our knowledge of light quark systems. A prescription for deriving an interaction linking these two limits has been developed by Buchmiiller, Grunberg and Tye (1980, 1981) and has been successfully applied to the IfJ and Y systems, leading them to suggest a value for the QCD scale parameter AMS" of 500 MeV. In this work we extend this formalism by incorporating the effects of allowing the virtual quarks which contribute to the interaction to have finite masses. These masses must be considered energy dependent, and it is found that while the properties of IfJ and Y states are insensitive to the detailed way in which the masses vary, the presence of mass thresholds has the effect of weakening the ability of this model to set the value of AMS ' with 500 MeV becoming an approximate lower bound.