Quantum construction of a unitary SU(2/1) model of the electro-weak interactions with 2 Higgs doublets

The interactions and even the number of the Higgs scalar fields are not fixed in the SU(2)U(1) standard model of the electro-weak interactions and the intrinsically chiral nature of the weak interactions is not explained. Embedding SU(2)U(1) into the Lie super-algebra SU(2/1) fills these gaps. The 2 smallest representations of SU(2/1) adequately describe the electron, neutrino, up and down quarks and correlate their chiralities with their U(1) charges, and the Higgs fields have the quantum numbers of the odd generators. But so far, there was an apparent conflict with unitarity, because the quark representation is not Hermitian and the super-Killing metric is not positive definite. We solve this paradox by assuming the existence of 2 complex Higgs doublets minimally coupled to the Fermions via the chiral projections of the odd generators of SU(2/1). We find that Lagrangian induced by the Fermion loops is unitary, thanks to the balance between the leptons and the quarks needed to cancel the triangle anomaly and that the super-Jacobi identity guarantees that the photon remains massless after symmetry breaking. In addition, the Lagrangian has a classical geometric interpretation in terms of the curvature of the corresponding Hermitian algebra. Assuming that the relative strength of the scalar and vector couplings does not depend on the number of families constrains the mass of the Higgs to $M^2_{H^0_1} + M^2_{H^0_2} = 32/9 M^2_W = 2 (107.2 GeV)^2$. Contrary to grand-unified or Wess-Zumino super-symmetric models, the SU(2/1) internal super-unification does not predict any unobserved particle besides the 2 Higgs doublets.