A Dark Sector Extension of the Almost-Commutative Standard Model

We consider an extension of the Standard Model within the frame work of Noncommutative Geometry. The model is based on an older model [St09] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from ~170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120-130 GeV. The short-coming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles

Almost-Commutative Geometry, massive Neutrinos and the Orientability Axiom in KO-Dimension 6

In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was that at least the orientability axiom of noncommutative geometry [5,6] may not be obeyed by the underlying geometry. In this publication we review three internal geometries, all three failing to meet the orientability axiom of noncommutative geometry. They will serve as examples to illustrate the nature of this lack of orientability. We will present an extension of the minimal standard model found in [7] by a right-handed neutrino, where only the sub-representation associated to this neutrino is not orientable

On Gravity, Torsion and the Spectral Action Principle

We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.Comment: minor modifications, some further typos fixe

On a Classification of Irreducible Almost-Commutative Geometries IV

In this paper we will classify the finite spectral triples with KO-dimension six, following the classification found in [1,2,3,4], with up to four summands in the matrix algebra. Again, heavy use is made of Kra jewski diagrams [5]. Furthermore we will show that any real finite spectral triple in KO-dimension 6 is automatically S 0 -real. This work has been inspired by the recent paper by Alain Connes [6] and John Barrett [7]. In the classification we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension six. By minimal version it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibitedComment: Revised version for publication in the Journal of Mathematical Physic

On a Classification of Irreducible Almost Commutative Geometries, A Second Helping

We complete the classification of almost commutative geometries from a particle physics point of view given in hep-th/0312276. Four missing Krajewski diagrams will be presented after a short introduction into irreducible, non-degenerate spectral triples.Comment: 11 page

The Inverse Seesaw Mechanism in Noncommutative Geometry

In this publication 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 to the classical AC model is the chiral nature of the AC fermions with respect to a U(1) 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 (ca. 1 GeV to 10^6 GeV). From this configuration a working inverse Seesaw mechanism for the neutrinos is obtained

On the noncommutative standard model

We propose a pedestrian review of the noncommutative standard model in its present state.Comment: dedicated to Alain Connes on the occasion of his 60th birthda