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At the classical level, the SU(2/1) superalgebra offers a natural descriptionof the elementary particles: leptons and quarks massless states, graded bytheir chirality, fit the smallest irreducible representations of SU(2/1). Ournew proposition is to pair the left/right space-time chirality with thesuperalgebra chirality and to study the model at the one-loop quantum level.If, despite the fact that they are non-Hermitian, we use the odd matrices ofSU(2/1) to minimally couple an oriented complex Higgs scalar field to thechiral Fermions, novel anomalies occur. They affect the scalar propagators andvertices. However, these undesired new terms cancel out, together with theAdler-Bell-Jackiw vector anomalies, because the quarks compensate the leptons.The unexpected and striking consequence is that the scalar propagator must benormalized using the antisymmetric super-Killing metric and the scalar-vectorvertex must use the symmetric d_aij structure constants of the superalgebra.Despite this extraordinary structure, the resulting Lagrangian is actuallyHermitian.

Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks