Covariant model of a quarkonium with the funnel potential

Abstract

The bound--state problem for the pion as a quarkonium with the funnel (Coulomb--plus--linear) interaction is solved in a framework that combines the bilocal approach to mesons with the covariant generalization of the instantaneous--potential model. The potential interaction leads to dynamical breaking of chiral symmetry. However, the Coulomb potential leads to ultraviolet divergences that must be subtracted. A careful choice of the renormalization prescription is needed in order to get the correct chiral limit. The mass, the lepton decay constant of the pion, as well as the pion decay width in two photons are calculated.