Relativistic Effects and the Confining Force in Heavy Quarkonia

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Abstract
Mass spectra, leptonic-decay rates and E1-transition rates of the charmonium and the bb system are investigated by using the instantaneous BS equation with flavor-independent confining forces. The cutoff in the transverse part of the gluon propagator is examined by considering the 4th-order quark-pair potential, and determined to be 1.5mq. In the case of the effective-vector confining potential, only rough models can be constructed even if one assumes the long-range tensor and/ or spin-spin forces. It is contrarily shown that the mass spectra are reproduced very well by the effective-scalar confining potential. Renormalized leptonic decay widths corrected by the hard-gluon contribution are consistent with the experiments in this model. E1-transition rates of ψ′→γχj are also consistent with the experimental values.

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