Christoph A. Stephan

Dark matter with invisible light from heavy double charged leptons of almost-commutative geometry?

A new candidate for cold dark matter arises from a novel elementary particle model: the almost-commutative AC-geometrical framework. Two heavy leptons are added to the standard model, each one sharing a double opposite electric charge and an own lepton flavour number. The novel mathematical theory of almost-commutative geometry (Connes 1994 Noncommutative Geometry (London: Academic)) wishes to unify gauge models with gravity. In this scenario two new heavy (mL ≥ 100 GeV), oppositely double charged leptons (A,C), (A with charge −2 and C with charge +2), are born with no twin quark companions. The model naturally involves a new U(1) gauge interaction, possessed only by the AC-leptons and providing a Coulomb-like attraction between them. AC-leptons posses electro-magnetic as well as Z-boson interaction and, according to the charge chosen for the new U(1) gauge interaction, a new invisible light interaction. Their final cosmic relics are bounded into neutral stable atoms (AC) forming the mysterious cold dark matter, in the spirit of the Glashows Sinister model. An (AC) state is reached in the early Universe along a tail of a few secondary frozen exotic components. They should be here now somehow hidden in the surrounding matter. The two main secondary manifest relics are C2+ (mostly hidden in a neutral (C2+e−e−) anomalous helium atom, at a 10−8 ratio) and a corresponding ion A2− bounded with an ordinary helium ion (4He)2+; indeed the positive helium ions are able to attract and capture the free A2− fixing them into a neutral relic cage that has nuclear interaction (4He2+A2−). The cage preserves the leptons to later recombine with neutral (C2+e−e−) into (AC) evanescent states. In early and late cosmic stages (AC) gas is leading to cold dark matter gravity seeds. It can form dense cores inside dense matter bodies (stars and planets). Binding (C2+e−e−) + (4He2+A2−) into (AC) atoms results in a steady decrease of the anomalous isotopes and a growing concentration of AC-gas. However the (AHe) influence on big bang nucleo-synthesis and catalysis of nuclear transformations in terrestrial matter appears to be a serious problem for the model. Moreover the zero lepton OLe-helium (AHe), (C2+e−e−) pollution and its on-going (AHe) catalysis in terrestrial waters may release frequent tens MeV gamma photons whose pair production leads to nearly aligned electron pairs; their consequent expected presence by twin Cherenkov rings poses a crucial test to the model. Their total absence in Super-Kamiokande or SNO records might point to the failure of the model, while their eventual discovery (above the background) may hint to the double charge AC-model to solve the cold dark matter puzzle. The new invisible light attraction allows us to stimulate the effective A–C recombination into (AC) atoms inside dense matter bodies (stars and planets), resulting in a decrease of anomalous isotopes below the experimental upper limits. OLe-helium pollution of terrestrial matter and (OHe) catalysis of nuclear reactions in it is one of the dramatic problems (or exciting advantages?) of the present model.

Almost-commutative geometries beyond the standard model

In Iochum et al (2004 J. Math. Phys. 45 5003), Jureit and Stephan (2005 J. Math. Phys. 46 043512), Schucker T (2005 Preprint hep-th/0501181) and Jureit et al (2005 J. Math. Phys. 46 072303), a conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this paper, a counter-example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle, these new particles provide a novel dark matter candidate.

On a classification of irreducible almost commutative geometries

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.

New scalar fields in noncommutative geometry

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 {approx}10{sup 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.

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 by Iochum, Schucker, and Stephan, J. Math. Phys. (to be published). Four missing Krajewski diagrams will be presented after a short introduction into irreducible, nondegenerate spectral triples.

Almost-commutative geometries beyond the standard model II: new colours

We will present an extension of the standard model of particle physics in its almost-commutative formulation. This extension is guided by the minimal approach to almost-commutative geometries employed by Iochum et al (2004 J. Math. Phys. 45 5003 (Preprint hep-th/0312276)), Jureit and Stephan (2005 J. Math. Phys. 46 043512 (Preprint hep-th/0501134)), Schucker (2005 Preprint hep-th/0501181), Jureit et al (2005 J. Math. Phys. 46 072303 (Preprint hep-th/0503190)) and Jureit and Stephan (2006 Preprint hep-th/0610040), although the model presented here is not minimal itself. The corresponding almost-commutative geometry leads to a Yang–Mills–Higgs model which consists of the standard model and two new fermions of opposite electromagnetic charge which may possess a new colour-like gauge group. As a new phenomenon, grand unification is no longer required by the spectral action.

The Spectral Action for Dirac Operators with Skew-Symmetric Torsion

We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the Riemann curvature tensor. Finally we deduce the Lagrangian for the Standard Model of particle physics in the presence of torsion from the Chamseddine-Connes Dirac operator.

Almost-commutative geometries beyond the standard model: III. Vector doublets

We will present a new extension of the standard model of particle physics in its almost-commutative formulation. This extension has as its basis the algebra of the standard model with four summands (Iochum et al 2004 J. Math. Phys. 45 5003 (Preprint hep-th/0312276), Jureit J-H and Stephan C 2005 J. Math. Phys. 46 043512 (Preprint hep-th/0501134), Schucker T 2005 Krajewski diagrams and spin lifts Preprint hep-th/0501181, Jureit et al 2005 J. Math. Phys. 46 072303 (Preprint hep-th/0503190), Jureit J-H and Stephan C 2006 On a classification of irreducible almost commutative geometries: IV (Preprint hep-th/0610040)), and enlarges only the particle content by an arbitrary number of generations of left–right symmetric doublets which couple vectorially to the U(1)Y × SU(2)w subgroup of the standard model. As in the model presented in Stephan (2007 Almost-commutative geometries beyond the standard model: II. New Colours Preprint hep-th/0706.0595), which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section.

Finding the standard model of particle physics a combinatorial problem

Abstract We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constraints. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang–Mills–Higgs models. Program summary Title of program: ko0 and ko6 Catalogue identifier: ADZZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZZ_v1_0.html Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4875 No. of bytes in distributed program, including test data, etc.: 29u2009933 Distribution format: tar.gz Programming language used: C++ Computer: Simple PC Operating system: Any, where C++ runs RAM: Depending on the global parameters ‘DIMENSION’ and ‘MAX_LEVEL’, a few KB to some MB Classification: 5, 11.1 Nature of problem: Automatised classification of almost-commutative geometries via Krajewski diagrams. Solution method: Combinatorial generation of all possible Krajewski diagrams and identification of the irreducible ones. Equivalence classes of irreducibles = classification. Running time: Depending on the global parameters ‘DIMENSION’ and ‘MAX_LEVEL’, running time reaches from seconds ( 3 × 3 ) to weeks ( 6 × 6 ) on a standard PC.

Seesaw and noncommutative geometry

The 1-loop corrections to the seesaw mechanism in the noncommutative Standard Model are computed. Other consequences of the Lorentzian signature in the inner space are summarised.