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The interactions and even the number of the Higgs scalar fields are not fixedin the SU(2)U(1) standard model of the electro-weak interactions and theintrinsically 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 2smallest representations of SU(2/1) adequately describe the electron, neutrino,up and down quarks and correlate their chiralities with their U(1) charges, andthe Higgs fields have the quantum numbers of the odd generators. But so far,there was an apparent conflict with unitarity, because the quark representationis not Hermitian and the super-Killing metric is not positive definite. Wesolve this paradox by assuming the existence of 2 complex Higgs doubletsminimally coupled to the Fermions via the chiral projections of the oddgenerators of SU(2/1). We find that Lagrangian induced by the Fermion loops isunitary, thanks to the balance between the leptons and the quarks needed tocancel the triangle anomaly and that the super-Jacobi identity guarantees thatthe photon remains massless after symmetry breaking. In addition, theLagrangian has a classical geometric interpretation in terms of the curvatureof the corresponding Hermitian algebra. Assuming that the relative strength ofthe scalar and vector couplings does not depend on the number of familiesconstrains 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-symmetricmodels, the SU(2/1) internal super-unification does not predict any unobservedparticle besides the 2 Higgs doublets.

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