Broken symmetries and leptonic weak interactions

Abstract

The currents involved in lepton-lepton couplings generate the algebra of U(4). Corresponding U(4)-algebras can be constructed from the hadron currents; they may be considered as subalgebras of higher symmetries like U(6) × U(6), etc. The U(4)-algebras are used for the construction of two models of a universal weak coupling. One model is based upon the U(4)-algebra generated by the total hadron current involved in semileptonic interactions, and a second one is obtained by considering strangeness-changing and nonchanging currents separately. The first model involves the Cabibbo angle as a parameter and it requires this angle to be the same for all currents. The second model has no such parameter; it depends upon a possible larger manifestation of the symmetry breaking interactions to account for the damping of ΔS = 1 transitions. In both cases the neutral generators of U(4) are identified with the 1 + γ 5)-projections of electromagnetic currents and of lepton number or triplet-number currents. For triplets with charges z + 1, z, z, the first model gives preference to z = 0 and the second one to z = −1. The two models are discussed briefly in connection with the phenomenological situation and with the assumption of broken SU(3)-symmetry for the hadrons. Renormalization effects are considered in detail, especially in view of the damping factor required in the second model mentioned above. The commutation relations of the hadron currents, together with the hypothesis of partially conserved axial-vector currents, give a reasonable universal damping factor λ A ∼ m π m K for axial vector matrix elements. For vector currents one obtains an analogous result only under rather restrictive assumptions. Otherwise, commutation relations, partially conserved currents, and λ V ∼ m π m K are not consistent as long as other manifestations of the symmetry breaker are considered to be small.