The Roots of the Standard Model of Particle Physics

Abstract

We conjecture how the particle content of the standard model can emerge starting with a supersymmetric Wess-Zumino model in 1+1 dimensions (d = 2) with three real boson and fermion fields. Considering SU(3) transformations, the lagrangian and its ground state are SO(3) invariant. The SO(3) symmetry extends the basic IO(1,1) Poincaré symmetry to IO(1,3) for the asymptotic fields requiring physical states to be singlets under the A_4 symmetry that governs the SO(3) embedding. This is linked to the three-family structure. For the internal symmetries of the asymptotic fields an SU(2) x U(1) symmetry remains, broken down as in the standard model. The boson excitations in d = 4 are identified with electroweak gauge bosons and the Higgs boson. Fermion excitations come in three families of leptons living in E(1,3) Minkowski space or three families of quarks living in E(1,1). Many features of the standard model now emerge in a natural way. The supersymmetric starting point solves the naturalness problem. The underlying left-right symmetry leads to custodial symmetry in the electroweak sector. In the spectrum one has Dirac-type charged leptons and Majorana-type neutrinos. The electroweak behavior of the naturally confined quarks, leads to fractional electric charges and the doublet and singlet structure of left- and right-handed quarks, respectively. Most prominent feature is the link between the number of colors, families and space directions.