Effective Description of a Composite Quark-Lepton Symmetry

We demonstrate the possibility that a basic [5U(2)]' symmetry of N subconstituents, which describes particle and antiparticle transitions, turns out to be at most an "effective" 50(2N) symmetry and at least an "effective" 5U( N) x UO) 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 50(2N) of composite operators constructed from the [5U(2)l'·operators acting on the composite quark· lepton states. The composite quarks and leptons are found to respect 50(4) X50(6) or 5U(2!IxU(1)Rx5U(3)c x UO!s-L according to a new selection rule, which is generated by the bilinear products of the raising and lowering operators of [5U(2)]'. This construction of the 50( 4) x 50( 6) generators allows us to uniquely define the five quantum numbers of this symmetry even at the subconstituent level. The full 50(10) generators can be also constructed; however, one needs a newly arranged "[5U(2)]5" symmetry only defined at the composite level, the generators of which turn out to be at most five body operators of the original [5U(2)]'.