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- 2009 (4) (remove)

We extend a classification of irreducible almost-commutative geometries, whose spectral action is dynamically nondegenerate, to internal algebras that have six simple summands. We find essentially four particle models: an extension of the standard model by a new species of fermions with vectorlike coupling to the gauge group and gauge invariant masses, two versions of the electrostrong model, and a variety of the electrostrong model with Higgs mechanism.

In this paper we will implement the inverse seesaw mechanism into the noncommutative framework on the basis of the AC extension of the standard model. The main difference from the classical AC model is the chiral nature of the AC fermions with respect to a U(1)(X) extension of the standard model gauge group. It is this extension which allows us to couple the right-handed neutrinos via a gauge invariant mass term to left-handed A particles. The natural scale of these gauge invariant masses is of the order of 10(17) GeV while the Dirac masses of the neutrino and the AC particles are generated dynamically and are therefore much smaller (similar to 1 to similar to 10(6) GeV). From this configuration, a working inverse seesaw mechanism for the neutrinos is obtained.

This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of Poincare duality. This defect may be repaired by adding new particles to the model, i.e., by building models beyond the standard model. The aim of this list of finite spectral triples (up to Poincare duality) is therefore to provide a basis for model building beyond the standard model.

In this publication we present an extension of the standard model within the framework of Connes' noncommutative geometry. The model presented here is based on a minimal spectral triple which contains the standard model particles, new vectorlike fermions, and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions, and the standard Higgs particle. The bosonic part of the action is given by the spectral action which also determines relations among the gauge couplings, the quartic scalar couplings, and the Yukawa couplings at a cutoff energy of similar to 10(17) GeV. We investigate the renormalization group flow of these relations. The low energy behavior allows to constrain the Higgs mass, the mass of the new scalar, and the mixing between these two scalar fields.