We consider the violation of the democratic mass matrix in the framework of the four-family standard model. Predictions of fourth-family fermion masses as well as quark and lepton CKM mixings are presented. Production and decay modes of new fermions are discussed. ͓S0556-2821͑96͒00819-3͔

The rare B s → φℓ + ℓ − decay is investigated by using the most general model independent effective Hamiltonian for ℓ = µ, τ . The calculated Br(B s → φµ + µ − ) = 1.92 × 10 −6 is in consistent with the experimental upper bound. The dependencies of the branching ratios and polarization asymmetries of leptons and combined leptonantilepton asymmetries on the new Wilson coefficients are presented. The analysis shows that the branching ratios and the lepton polarization asymmetries are very sensitive to the scalar and tensor type interactions. The results obtained in this work will be very useful in searching new physics beyond the standard model. *

The rare B c → D s ℓ + ℓ − decay is investigated by using the most general model independent effective Hamiltonian. The general expressions of longitudinal, normal and transversal polarization asymmetries for ℓ − and ℓ + and the combined asymmetries of them are found. The dependencies of the branching ratios and polarizations on the new Wilson coefficients are presented. The analysis shows that the branching ratios and the lepton polarization asymmetries are very sensitive to the scalar and tensor type interactions. These results will be very useful in searching new physics beyond the standard model.

The rare semileptonic Bc → D * s ℓ + ℓ − decay is studied in the scenario of the universal extra dimension model with a single extra dimension in which inverse of the compactification radius R is the only new parameter. The sensitivity of differential branching ratio, total branching ratio, polarization and forward-backward asymmetries of final state leptons, both for muon and tau, to the compactification parameter is presented. For some physical observables uncertainty on the form factors and resonance contributions have been considered in the calculations. Obtained results, compared with the available data, show that there appear new contributions due to the extra dimension. *