Weak Interaction Based on the Three-Triplet Model: Simple Product of Charged Current

Abstract

On the basis of the three-triplet model of hadrons, we investigate the structure of weak interaction constructed as charged current × charged current. The hadronic current is a linear combination of (8,1), (1,8) and (8,8) components of SU(3)’ ⊗SU(3)″, and the leptonic current is the usual one. General constraints are given under which weak interaction responsible for nonleptonic decays has no (27,1) representation. As differences between the ordinary interaction (Cabibbo theory) and interaction considered here appear in the matrix elements of the hadronic current products, we investigate properties of Adler-type and Gross-Smith-type sum rules for nucleon target and the nonleptonic interaction of ordinary hadrons. The following results are obtained: (1) Even if the (27,1) vanishing condition is satisfied, the Adler sum rules for nucleon target can be obtained. (2) It is possible to construct HW by the hadronic current which satisfies the closed-algebra and the (27,1) vanishing conditions. (3) The Adler sum rules cannot be obtained if the (27,1) vanishing and the closed-algebra conditions are imposed. (4) Under the (27,1) vanishing condition, the Gross-Smith sum rules cannot be obtained. (The values of the Gross-Smith-type integral are larger in magnitude than the original ones.) (5) If the value of \int10(Fνp2(x)-Fνn2(x))dx/x is larger than that in the usual theory, the value of \int10(Fνp2(x)-Fνn2(x))dx/x is larger than that in the usual theory. We discuss how to select various possibilities of weak interactions (the present model, our previous model and the Cabibbo theory).