Dynamical Generation of a Composite Quark-Lepton Symmetry

摘要

We demonstrate the possibility that a basic (SU(2))sup(N) symmetry of N subconstituents, which describes particle and antiparticle transitions, generates at most an ''effective'' SO(2N) symmetry and at least an ''effective'' SU(N) x U(1) symmetry of composite quarks and leptons whose states are specified by the N different kinds of subconstituents. The generators of the ''effective'' symmetry, are identified by the correct algebraic properties specific to SO(2N) of composite operators constructed from the (SU(2))sup(N)-operators acting on the composite quark-lepton states. The composite quarks and leptons are found to respect SO(4) x SO(6) or SU(2)sub(L) x U(1)sub(R) x SU(3)sub(c) x U(1)sub(B-L) according to a new selection rule, which are generated by the bilinear products of the raising and lowering operators of (SU(2)) exp 5 . This construction of the SO(4) x SO(6) generators allows us to uniquely define the five quantum numbers of that symmetry even at the subconstituent level. The full SO(10) generators can be also constructed; however, one needs a newly arranged (SU(2)) exp 5 symmetry only defined at the composite level, the generators of which turn out to be at most N body operators of the original (SU(2)) exp 5 . (Atomindex citation 14:722670)