In the extended SUc(3) x SUL(2) x U (1) x SUf (3) Standard Model, there are the family Higgs fields Phi(3,2) and Phi(3,1) on top of the Standard-Model Higgs Phi(1,2) [with the first SUf (3) label and the SUL(2) one]. The neutral part of Phi(3,2) all have the vacuum expectation values, accounting for neutrino oscillations. Since all family gauge bosons are massive, only one component of the six in Phi(3,1) gets a vacuum expectation value. Under such scenario, we analyze the expanded Higgs mechanism - concluding that the cancelations among all the Higgs and super-symmetric partners might not be there. We suggest that the dimensional regularization to the non-integer dimensions (d not equal 4), which renders finite the ultraviolet divergences, could be analyzed to yield the proper scenario. In particular, we suggest that, for the quadratic divergence diagrams which give rise to blow-up behaviors, the overall cancelation should occur, in a complete Standard Model (such as our extended Standard Model which we believe so), in a certain way. Furthermore, we discuss the connections of reactions in neutrino oscillations and in lepton-flavor violations, since these lepton-flavor-violating reactions or decays might offer another decisive tests of the Standard Model.
