Lie groups with the same Lie algebra as the standard model but different global topology are considered, and the possibilities are reduced to four viable alternatives for the true symmetry group of the standard model: SU(3)×SU(2)×U(1), U(3)×SU(2), SU(3)×U(2), and S(U(3)×U(2)). It is demonstrated that the last three groups require hypercharge quantization for their allowable representations, and that S(U(3)×U(2)) is the most likely candidate for the true symmetry group of the standard model because it offers the best explanation of the observed hypercharges of the elementary fermions. Explicit S(U(3)×U(2)) tensor representations of the quarks and leptons are given and are compared to the standard SU(5) assignments. The spontaneous symmetry breaking of S(U(3)×U(2)) to an electrostrong U(3) is briefly discussed, and electric charge quantization follows from weak hypercharge quantization and the existence of the standard Higgs doublet with nonzero vacuum expectation value. Lastly, it is shown that combining the conditions imposed by anomaly cancellation with the S(U(3)×U(2)) hypercharge quantization condition uniquely determines the ratios of the hypercharges in a standard quark-lepton family.
Physical Review D
- Pub Date:
- April 1991
- Charge conjugation parity time reversal and other discrete symmetries;
- Other internal and higher symmetries;
- Unified theories and models of strong and electroweak interactions