A Dualized Standard Model recently proposed affords a natural explanation for the existence of Higgs fields and of exactly 3 generations of fermions, while giving at the same time the observed fermion mass hierarchy together with a tree-level CKM matrix equal to the identity matrix. It further suggests a method for generating from loop corrections the lower generation masses and nondiagonal CKM matrix elements. In this paper, the proposed calculation is carried out to 1-loop. It is found first that with the method suggested one can account readily for the masses of the second generation fermions as a 'leakage' from the highest generation. Then, with the Yukawa couplings fixed by fitting the masses of the 2 higher generations, one is left with only 2 free parameters to evaluate the CKM matrix and the masses in the lowest generation. One obtains a very good fit to the CKM matrix and sensible values for the masses of d and e, though, for a valid reason, not of u. In addition, the fitted values of the Yukawa couplings and vacuum expectation values of the dual colour Higgs fields show remarkable features perhaps indicative of a deeper significance.

The Dualized Standard Model which gives explanations for both fermion generations and Higgs fields has already been used to calculate fermion mass and mixing parameters with success. In this paper, we extend its application to low energy FCNC effects deriving bounds for various processes in terms of one single mass scale. Using then experimental information from K L − K S mass difference and air showers beyond the GZK cut-off, these bounds are converted into rough, order-of-magnitude predictions. In particular, the estimates for the decay K L → e ± µ ∓ and for the mass difference between the neutral D-mesons seem accessible to experiment in the near future.

It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transportà µ (x) constructed earlier for monopoles is seen to function also as a potential in giving a full description of the gauge field, playing thus an entirely dual symmetric role to the usual potential A µ (x). Sources of A are monopoles ofà and vice versa, and the Wu-Yang criterion for monopoles is found to yield as equations of motion the standard Wong and Yang-Mills equations for respectively the classical and Dirac point charge; this applies whether the charge is electric or magnetic, the two cases being related just by a dual transform. The dual transformation itself is explicit, though somewhat complicated, being given in terms of loop space variables of the Polyakov type.

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The classic question of a nonabelian Yang-Mills analogue to electromagnetic duality is here examined in a minimalist fashion at the strictly 4-dimensional, classical field and point charge level. A generalisation of the abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the abelian theory. For example, there is a dual potential, but it is a 2-indexed tensor T µν of the Freedman-Townsend type. Though not itself functioning as such, T µν gives rise to a dual parallel transport,à µ , for the phase of the wave function of the colour magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard colour (electric) charge itself is found to be a monopole ofà µ . At the same time, the gauge symmetry is found doubled from say SU (N ) to SU (N ) × SU (N ). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a 'universal' principle, namely the Wu-Yang (1976) criterion for monopoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov (1980).