Octet dominance in nonleptonic decays

The question of octet enhancement for the nonleptonic decays is studied within the framework of a current-algebra approach. By writing an unsubtracted dispersion relation for the matrix elements 〈B_k|H_w|B_j〉 and 〈M_k|H_w|M_j〉 (B denoting a $\text{1}\text{2}{}^{\mathrm{+}}$ baryon and M a 0^? meson) in the momentum transfer squared variable t and using the assumption of threshold dominance, namely that two pseudoscalar meson states dominate the absorptive parts of the above matrix elements and that in the chiral limit the meson-baryon and meson-meson scattering amplitudes which enter in the absorptive parts are exactly given by current algebra low energy theorems, it is shown that the above matrix elements are octet enhanced without assuming the octet transformation property for H_w. Further it is shown that the $\text{d′}\text{f′}$ ratio for the octet enhanced matrix elements 〈B_k|H_w|B_j〉 satisfies the relation , where $\text{(}\text{f}\text{d}\text{)}{}_{\mathrm{A}}$ denotes the $\text{f}\text{d}$ ratio of the axial vector current baryon couplings. The implications of this result for the s- and p-wave hyperon non-leptonic decays are discussed.