Unlocking the Standard Model; N=1 and 2 generations of quarks : spectrum, mixing and symmetries

The Glashow-Salam-Weinberg model for N=2 generations is extended to 8 composite Higgs multiplets by using a one-to-one correspondence between its complex Higgs doublet and very specific quadruplets of bilinear quark operators. This is the minimal number required to suitably account, simultaneously, for the pseudoscalar mesons that can be built with 4 quarks and for the masses of the $W$ gauge bosons. They are used as input, together with elementary low energy considerations, from which all other parameters, masses and couplings can be calculated. We focus in this work on the spectrum of the 8 Higgs bosons, on the mixing angles, and on the set of horizontal and vertical entangled symmetries that, within the chiral $U(4)_L times U(4)_R$ group, strongly frame this extension of the Standard Model. In particular, the $u-c$ ($theta_u$) and $d-s$ ($theta_d$) mixing angles satisfy the robust relation $tan(theta_d+theta_u)tan(theta_d-theta_u) = Big(frac{1}{m_{K^pm}^2}-frac{1}{m_{D^pm}^2}Big) big/ Big(frac{1}{m_{pi^pm}^2}-frac{1}{m_{D_s^pm}^2}Big)$. Light scalars (below $90 MeV$) arise and the mass of (at least) one of the Higgs bosons grows like that of the heaviest $bar qgamma_5 q$ bound state. $theta_u$ cannot be safely tuned to zero and several parameters have no reliable expansion in terms of small parameters like $m_pi$ or the mixing angles. This study does not call for extra species of fermions. The effective couplings of scalars, which depend on the non-trivial normalization of their kinetic terms, can be extremely weak. For the sake of (relative) brevity, their rich content of non-standard physics (including astrophysics), the inclusion of the 3rd generation and the taming of quantum corrections are left for a subsequent work.