Toponium as Nonabelian Positronium ?

Abstract

The expected large mass $m_t$ of the top quark provides for the first time a chance to discuss the bound-states of the corresponding quantum system as the nonabelian generalization of positronium, using the full power of relativistic quantum field theoretic methods which are available for weakly bound systems. Thus our approach differs in principle from the one used in the vast phenomenological literature on quarkonium potentials. We emphasize especially the corrections of energy levels which are of order $\a^4 m_t$ or numerically comparable to that order, and which have no counterpart in the 'relativistic' corrections of QED. In contrast to previous computations we give analytic expressions for all contributions considered in our present work, hopefully preparing the ground for further similar calculations.