Dynamical Basis of the Sum Rule2Ξ−−=Λ−0+3Σ0+. II

The assumptions that (1) the weak processes $B\to B^{\prime }$, $M\to M^{\prime }$ ($\Delta S=\pm 1$) are mediated by an interaction that transforms like ${\lambda }_6$, (2) the nonleptonic decay amplitudes of hyperons are dominated by pole terms, and (3) the mass-splitting pattern of the baryon octet can be approximated by $m=m_0+\left(\Delta m\right)Y$ imply that the effective Lagrangian describing the parity-conserving hyperon decays transforms like ${\lambda }_{\tau }$ under $\mathrm{SU}\left(3\right)\mathrm{}$. The sum rule $2P\left(\Xi _{-}^{}{}_{}{}^{-}\right)=P\left(\Lambda _{-}^{}{}_{}{}^0\right)+\sqrt{3}P\left(\Sigma _0^{}{}_{}{}^{+}\right)$ follows immediately from this observation.