Renormalization of QQ Annihilation Vertex in Dirac Hydrogen Type Quarkonium

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Abstract
The QQ̄ annihilation vertices in the Dirac hydrogen type system are calculated analytically with corrections of all orders of the Coulomb type interaction. Using this, the renormalized QQ̄ vertices of the type of vector and axial vector are obtained and GAR = GVR is shown. We also obtain the decay constant of the Dirac hydrogen type quarkonium. The renormalized vertex is shown to satisfy the asymptotic freedom. It is left an open question to determine the renormalized weak coupling constant in our model.