Tracing the Gauge Origin of Yukawa and Higgs Parameters Beyond the Standard Model

We discuss possible realizations of the hypothesis that all the fundamental interactions of the elementary particles should be of gauge type, including the Yukawa and Higgs ones. In the minimal SUSY extension of the standard model, where the quartic Higgs couplings are ``gauged'' through the D-terms, it is also possible to generate radiatively the Yukawa matrices for the light generations, thus expressing them as functions of gauge couplings. The program can also be applied to the SUSY LR model, where the possibility to induce radiatively the mixing angles, can help to make viable the parity solution to the strong CP problem. The superpotential of the model still includes some non-gauge couplings, namely, the Yukawa for the third generation and the trilinear terms involving the Higgs bi-doublet and two pairs of doublets. Additional progress to relate these parameters to gauge couplings, can be made by embedding the LR model within a SUSY model SU(4)_WxU(1)_{B-L} in five dimensions, where the Higgs bi-doublet is identified as the extra component of the 5D gauge field.