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

Abstract

At the classical level, the SU(2/1) superalgebra offers a natural description of the elementary particles: leptons and quarks massless states, graded by their chirality, fit the smallest irreducible representations of SU(2/1). Our new proposition is to pair the left/right space-time chirality with the superalgebra 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 of SU(2/1) to minimally couple an oriented complex Higgs scalar field to the chiral Fermions, novel anomalies occur. They affect the scalar propagators and vertices. However, these undesired new terms cancel out, together with the Adler-Bell-Jackiw vector anomalies, because the quarks compensate the leptons. The unexpected and striking consequence is that the scalar propagator must be normalized using the antisymmetric super-Killing metric and the scalar-vector vertex must use the symmetric d_aij structure constants of the superalgebra. Despite this extraordinary structure, the resulting Lagrangian is actually Hermitian.