Successful renormalization of a QCD-inspired Hamiltonian

Abstract

The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. The formalism is applied to physical mesons with a different flavor of quark and anti-quark. The excitation spectrum of the ρ-meson with its excellent agreement between theory and experiment is discussed as a pedagogical example.Reverting the argument, one concludes as in [20] that the oscillator model in Eq.(22) explains quite naturally the systematics found by Anisovich et al. [22]. Relating the oscillator model to QCDThe oscillator model in Eq. (22) is only the harmonic approximation to the QCD-inspired, generalized Coulomb potential in Eq.(20). Their parameters are related obviously by c t = −α c λa, b = 0, and