An Application of SU3 Group to the Theory of Weak Interactions

Abstract

A theory of strong and weak interactions is proposed. Strong interactions are assumed to be invariant under an SU3 group Gs and Gell-Mann's scheme is adopted for baryons. Weak interactions are postulated to be invariant under an SU3 group (or an u~ group) Gw which is closely related to the group Gs. Invariance under the CR-conjugation is required for both strong and weak interactions. The and axial-vector part of baryon currents are then determined to be of F- and D-type, respectively. Consequently, i) the parts of baryon currents are conserved and ii) the coupling between pseudoscalar octet bosons and baryons is of D-type, if Goldberger-Treiman relation holds. It is shown that a special case of our theory is partly equivalent to a Cabibbo's model. 1 ) The general theory of gauge transformation is applied to this model using a pair of spurions of an SU3 group and intermediary mesons. Accordingly, oS/oQ= -1 transitions do not exist. As a hopeful example, a nine-fold way of leptons is proposed where weak interactions are quite symmetrical in baryonic and leptonic multiplicities. This model requires the existence of four new leptons (two charged and two neutral) with non-zero mass and several intermediary mesons. The charged new leptons decay rapidly and, consequently, the detection of these new leptons is difficult at present time. The oS = 0 and oS /oQ = 1 interactions are of scalar coupl­ ing and of vector coupling for the group Gw, respectively. It is shown that oSjoQ= -1 transitions can also be present in this model as an interaction of vector coupling for the group Gw.