Rescattering Effects in the Quark Model for Meson-Baryon Couplings

The eikonal approximation in high-energy scattering is used as a basis for the evaluation of scattering corrections to meson-baryon couplings in the independent quark model. These corrections, which reduce the $\mathrm{SU}\left(6\right)\mathrm{}$ symmetry (characteristic of the impulse approximation) to a mere $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry, are found to be typically of the order of 20-30% on the coupling constants. An important part of the correction, which arises from the purely "$\mathrm{SU}\left(3\right)\mathrm{}$-isotropic" component of the meson-quark amplitude, has exactly the same structure as the $\mathrm{SU}\left(6\right)\mathrm{}$-invariant couplings and hence can be interpreted as a renormalization effect. The remaining corrections, which may be called the "true scattering effects," lead to an explicit formula for the $\frac{F}{D}$ ratio in octet couplings in terms of the meson-quark scattering parameters which differs from its $\mathrm{SU}\left(6\right)\mathrm{}$ value of $\frac{2}{3}$ by about 4%. These corrections also give an enhancement factor for decuplet decays which increases the predicted rate for $N^{*}\to N\pi$ by about 30%. It is argued that the nature of these numerical results is rather insensitive to the precise validity or lack of validity of the eikonal approximation.