Horizontal symmetry and the fourth generation

A systematic investigation of all possible horizontal symmetries acting on four generations of quarks in a minimal left-right-symmetric model is carried out. There are only two consistent models with realistic constraints on the quark masses and mixing angles. It is shown that Z4 is the unique symmetry group leading to these models. The fourth-generation quark masses m/sub b//sub '/ and m/sub t//sub '/ are constrained to be (A) m/sub b//m/sub t/≅m/sub b//sub '//m/sub t//sub '/, (B) m/sub s//m/sub c/≅(m/sub b/+m/sub b//sub '/)/(m/sub t/+m/sub t//sub '/). Thus, model (A) predicts m/sub t/,m/sub b//sub '/≤43 GeV whereas model (B) has m/sub b//sub '/≤58 GeV. The two models differ in the mixing of the fourth generation into the first three. A crucial test which can distinguish the two models is a direct measurement of the mixing matrix element chemical bondV/sub u//sub b/chemical bond. Model (A) predicts it to be ∼10/sup -4/, an order of magnitude smaller than the prediction of model (B)