Flavor unification

The present unified field theories--namely, (i) the SU(2)/sub L/(X)U(1) theory of the weak and electromagnetic interactions and (ii) the SU(5) grand unified theory--treat fermions in terms of families. This is because these are incomplete theories. We attempt flavor unification by introducing a ''horizontal'' gauge group. At the level of the weak and electromagnetic interactions we conjecture that the b-quark could decay dominantly via the horizontal interactions. Bounds are derived on the lifetime of the b-quark and B0-anti B0 mixing, assuming this to be true. The multilepton signature for such a scenario in the decay of upsilon is evaluated. It is shown that the multilepton events get related to the branching ratios for the decay of the tau-lepton. Next we investigate the problem of incorporating the flavor generations within the framework of a grand unified SU(N) gauge theory. The requirement of no triangle anomaly and an asymptotically free gauge coupling constant appears to limit the number of ''light'' fermion generations to four. Specializing to an SU(8) model, we exhibit a Higg's mechanism that splits the fermions into heavy and light sets, the later containing only three generations. We argue that the mass of the heavy generations is in the Tev region. We discuss the radiative effects on the Weinberg angle in such theories. Further using one loop renormalization group equations we obtain the scale at which the flavor-grand unification occurs. We argue that logical completeness requires that we consider SU(10) and SO(15) gauge groups as serious candidate theories