About the Bethe Salpeter Formalism in the Heavy Mass Limit

Details About the Bethe Salpeter Formalism in the Heavy Mass Limit About the Bethe Salpeter Formalism in the Heavy Mass Limit

1994-03-02

arxiv.org/abs/hep-ph/9403207v1

Z.Phys.C63:569-574,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, (4 figures available on request), OUTP - 94 01P

Scientific paper

10.1007/BF01557622

We investigate the Bethe--Salpeter description of mesons in the limit where one of the constituing quarks is infinitely heavy. To recover the non--relativistic quark model out of the Bethe--Salpeter formalism it is usual to assume that the potential is instantaneous and the Fock space is reduced to $Q\bar{q}$ states. We show that in the Feynman gauge in perturbation theory and for a heavy quark being on--mass shell the instantaneity of the potential is valid in the rest--frame of the meson. Furthermore we argue that to first order in the velocity exchange during a heavy meson transition, the error induced by the reduction of the Fock--space is small. This in turn justifies quark model calculations, even when one quark is light.

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