SU(3)Symmetry-Breaking Interactions

Abstract

It is proposed that all symmetry-breaking interactions ${H}^{i}$ are of the current-current form, and a calculational method suitable for obtaining sum rules is developed. The method essentially is to express the matrix elements of ${H}^{i}$ in terms of the matrix elements of the double commutator of ${H}^{i}$ with $\mathrm{SU}(3)$ generators. When the method is combined with the technique of reducing a pion, it can be shown that the $S$-wave amplitudes of both the triangle relation and the Lee-Sugawara relation of nonleptonic decays correspond to sum rules of photonic decay amplitudes and semileptonic decay amplitudes of hyperons.