Unlocking the Standard Model. IV. N=1 AND 2 generations of quarks : spectrum and mixing

Using a one-to-one correspondence between its complex Higgs doublet and very specific quadruplets of bilinear quark operators, the Glashow-Salam-Weinberg model for 2 generations is extended, without adding any extra fermion, to 8 composite Higgs multiplets. 8 is the minimal number required to suitably account, simultaneously, for the pseudoscalar mesons that can be built with 4 quarks and for the mass of the W gauge bosons. Their masses being used as input, together with elementary low energy considerations for the pions, we calculate all other parameters, masses and couplings. We focus in this work on the spectrum of the 8 Higgs bosons, and on the two u-c and d-s mixing angles, showing that this is very fine-tuned physics. We show in particular that the u-c mixing angle cannot be safely tuned to 0. Symmetries are investigated in detail. We leave the study of couplings and of their content of non-standard physics to a forthcoming work.