African Journal of Mathematical Physics

AJMP Volume 3 Number 1 (2006)

 Home AJMP Volume 10 Number 1 AJMP Volume 9 Number 1 AJMP Volume 8 Number 1 AJMP Volume 7 Number 1 AJMP Volume 6 Number 1 AJMP Volume 5 Number 1 AJMP Volume 4 Number 1 AJMP Volume 3 Number 1 AJMP Volume 2 Number 2 AJMP Volume 2 Number 1 AJMP Volume 1 Number 2 AJMP Volume 1 Number 1
Research Papers

Title: Supersymmetry becomes precision physics
Author: Wolfgang Hollik
Abstract:
Precision calculations in the frame of in the minimal supersymmetric standard model are reviewed for (i) electroweak precision observables, (ii) Higgs boson masses, and (iii) supersymmetric particle masses, production cross sections and decay rates.

Title: Lattice QCD Study for Confinement and Hadrons
Authors: Hideo Suganuma, Hiroko Ichie, Fumiko Okiharu and Toru T. Takahashi
Abstract:
Using SU(3) lattice QCD, we perform the detailed studies of the three-quark and the multi-quark potentials. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{ 3Q}^{ g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1\%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation for the 1st excited-state 3Q potential $V_{3Q}^{e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three quarks, and find a large gluonic-excitation energy $\Delta E_{ 3Q} \equiv V_{3Q}^{ e.s.}-V_{3Q}^{g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model. $\Delta E_{3Q}$ is found to be reproduced by the “inverse Mercedes Ansatz”, which indicates a complicated bulk excitation for the gluonic-excitation mode. We study also the tetra-quark and the penta-quark potentials in lattice QCD, and find that they are well described by the OGE Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks.

Title: Local Currents for a Stable Algebra of Quantum Mechanics
Authors: Gerald A. Goldin and Sarben Sarkar
Abstract:
Beginning with nonrelativistic local current algebra in two space dimensions, we show how to recover a certain deformed algebra of quantum mechanics in one space dimension discussed by Vilela Mendes, having a fundamental length scale $\ell$. The extra dimension becomes an unobservable internal degree of freedom in the $\ell \to 0$ limit. This hints at a new possible interpretation of representations of the local current algebra, not as describing conventional bosonic, fermionic, or anionic particles in two-space, but as describing systems having such features in the deformed one-dimensional quantum mechanics. We also look at discretized local currents within irreducible representations of the deformed algebra
Title: A QFT Realisation of Kac-Moody Theory of Lie Algebras
Authors: El Hassan Saidi
Abstract:
We construct the structure of a graded $q$-differential algebra on a ${\bf Z}_N$-graded algebra by means of a graded $q$-commutator. We apply this construction to a reduced quantum plane and study the first order differential calculus on a reduced quantum plane induced by the $N$-differential of the graded $q$-differential algebra.
Title: Non-perturbative Results for QED on Non-commutative Spaces
Authors: W. Bietenholz, A. Bigarini, F. Hofheinz, J. Nishimura, Y. Susaki and J. Volkholz
Abstract:
We present non-perturbative results for $U(1)$ gauge theory in spaces, which include a non-commutative plane. In contrast to the commutative space, such gauge theories involve a Yang-Mills type interaction term. The Wilson loop is complex on the non-perturbative level. We first consider the 2d case: small Wilson loops are (almost) real and follow an area law, whereas for large Wilson loops the complex phase rises linearly with the area. In $d=4$ the behaviour is qualitatively similar for loops in the non-commutative plane, whereas the loops in other planes follow closely the commutative pattern. In both cases we also discuss the extrapolation of our results to the continuum and infinite volume by means of a Double Scaling Limit.

### AJMP/0606 [ ps, pdf] :

Title: Charged Open Strings in a Background Field and Euler-Heisenberg Effective Action
Authors: Stefano Sciuto
Abstract:
This talk is based on work made with L. Magnea and R. Russo \cite{noi}. We give an explicit expression of the multiloop partition function of open bosonic string theory in the presence of a constant gauge field strength. The Schottky parameterization allows to perform the field theory limit, which at two-loop level reproduces the Euler-Heisenberg effective action for adjoint scalars minimally coupled to the background gauge field.
Title: Spectral Geometry: Case of Quantum Spheres
Authors: Andrzej Sitarz
Abstract:
We review the ideas of noncommutative spectral geometry a la Connes and illustrate it with an example of quantum two-sphere.
Title: Approach Unifying Spins and Charges in d=14 Predicts Properties of Four Families of Quarks and Leptons
Authors: N. Mankoc Borstink

Abstract:
Ten years ago the approach unifying all the internal degrees of freedom -that is the spin and all the charges into only the spin - was proposed \cite{norma92-portoroz03}. In this approach spinors, living in $d (=1+13)-$dimensional space, carry only the spin and interact with only the gravity through spin connections and vielbeins. After assuming appropriate breaks of symmetries a spin manifests in $d\=(1+3)$ ''physical'' space as the spin and all the known charges, while the covariant derivative of a spinor in $d(=1+13)-$ manifests as the observable covariant derivative in $d=1+3$ and as the mass terms, leading to masses of four families of quarks and leptons and to the corresponding mixing matrices.
AJMP/0609[ ps,pdf] :
Title: Perturbative Approach to $U_A(1)$ Breaking
Authors: Brigitte Hiller, Alexander A. Osipov, Alex H. Blin

Abstract:

The six-quark instanton induced 't Hooft interaction is considered in combination with the Nambu-Jona-Lasinio (NJL) type $U_L(3)\times U_R(3)$ chiral symmetric Lagrangian. We discuss the bosonization of this multi-quark interaction, taking the $U_A(1)$ breaking as a perturbation. We discuss its relation with the usual approach
Title: Supersymmetric Models and CP Violation in B Decays
Authors: Shaaban Khalil
Abstract:
In this talk CP violation in the supersymmetric models, and especially in $B$ -decays is discussed. We review our analysis of the supersymmetric contributions to the mixing CP asymmetries of $B\to \phi K_S$ and $B\to \eta^{\prime} K_S$ processes. Both gluino and chargino exchanges are considered in a model independent way by using the mass insertion approximation method. The QCD factorization method is used, and parameterization of this method in terms of Wilson coefficients is presented in both decay modes. Correlations between the CP asymmetries of these processes and the direct CP asymmetry in $b\to s \gamma$ decay are shown.
discuss its relation with the usual approach.
AJMP/0611[ ps, pdf] :
Title: Complete one--loop: to stop and sbottom decays into $Z$ and $W^{\pm}$ bosons
Authors: Abdesslam Arhrib and Rachid Benbrik
Abstract:
The complete one--loop radiative corrections to third generation scalar fermions into gauge bosons $Z$ and $W^\pm$ is considered. We focus on $\wt{f}_2 \to Z \wt{f}_1$ and $\wt{f}_i \to W^\pm \wt{f}_1^\prime$, $f,f^\prime =t,b$. We include both SUSY-QCD, QED and full electroweak corrections. It is found that the electroweak corrections can be of the same order as the SUSY-QCD corrections. The two sets of corrections interfere destructively in some region of parameter space. The full one loop correction can reach 10\% in some SUGRA scenario, while in model independent analysis like general MSSM, the one loop correction can reach 20\% for large $\tan\beta$ and large trilinear soft breaking terms $A_b$.
Title: Solving the $B\to\pi\pi$ and $B\to\pi K$ puzzles
Authors: Stefan Recksiegel
Abstract:
Gravity and quantum physics become inseparable at the Planck scale. This leads to the expectation that the space-time metric itself behaves as a quantum variable. In the present work, this behavior is modeled as conformal variations about the classical background metric. The scalar field which describes these variations represents the quantum fluctuations; it is treated in lowest order by employing the classical variation principle. Variation of the gravitational action leads thus to a modified Einstein equation, where the new extra term is interpreted as a cosmological constant. The resulting equation of motion for the expanding universe is capable of accommodating the current observational data, which indicate an accelerating expansion during the current epoch.
AJMP/0613[ ps, pdf] :

Title: Some Remarks on Tree-Level Vacuum Stability in Two Higgs Doublet Models
Authors: A. Barroso, P.M. Ferreira and R. Santos
Abstract:
It is proved that the minimum of a general two Higgs doublet model's potential is stable at tree level. A relation between stability and flavor changing neutral currents at tree level is shown.

AJMP/0614[ ps, pdf] :
Title: Signatures of Collisional Annihilation in Ultra-High Energy Cosmic Rays
Authors: Rainer Dick, Karla M. Hopp, Kai E. Wunderle
Abstract:
We first review the motivations and main aspects of the proposal that ultra high energy cosmic rays originate in collisional annihilation of superheavy dark matter particles in our galactic halo. We then emphasize that the various proposals for the origin of ultra high energy cosmic rays predict qualitatively different patterns of arrival directions for primary cosmic ray energies beyond the GZK bound. We expect that in about three years the anisotropy signal observed by the Pierre Auger observatory will tell us which proposal was correct.
AJMP/0615[ ps, pdf] :
Title: Planck Scale Variations of the Metric Tensor Leading to a Cosmological Constant
Authors: Alex H. Blin
Abstract:
Gravity and quantum physics become inseparable at the Planck scale. This leads to the expectation that the space-time metric itself behaves as a quantum variable. In the present work, this behavior is modeled as conformal variations about the classical background metric. The scalar field which describes these variations represents the quantum fluctuations; it is treated in lowest order by employing the classical variation principle. Variation of the gravitational action leads thus to a modified Einstein equation, where the new extra term is interpreted as a cosmological constant. The resulting equation of motion for the expanding universe is capable of accommodating the current observational data, which indicate an accelerating expansion during the current epoch.
AJMP/0616[ ps, pdf] :
Title: Anharmonic Oscillator Hamiltonian and Multiple Scale Techniques
Authors: M. Capdequi Peyranère
Abstract:
A multiple scale technique is applied to the quantum anharmonic oscillator in the Heisenberg picture, leading to interesting features of the solution of the Heisenberg equations of motion and of the Hamiltonian spectrum. Remarks on the classical case are also sketched.
Title: Extension of the Poincar\'e Symmetry for $p-$ Forms
Authors: G. Moultaka, M. Rausch de Traubenberg and A. Tanasa
Abstract:
A non-trivial extension of the $D-$dimensional Poincaré algebra is investigated. It is shown that this extension acts in a natural geometric way on antisymmetric gauge fields or $p-$forms. Some field theoretical aspects of this symmetry are studied and invariant Lagrangians are explicitly given.
AJMP/0618[ ps, pdf] :
Title: Confining Interquark Potentials Driven by Scalar Field in Non Abelian Gauge Theories: A Review
Authors: M. Chabab, L. Sanhaji
Abstract:
In this review paper, we revisit in Part I some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. In part II, we solve the semi-relativistic wave equation, for Dick interquark potential using the Shifted-$l$ expansion technique (SLET) in the heavy meson sector. The results of this study proves that phenomenological investigation of this mechanism is more than justified and deserves more efforts.
AJMP/0619[ ps, pdf] :
Title: Carnot-Carathéodory Metric vs Gauge Fluctuation in Noncommutative Geometry
Authors: Pierre Martinetti
Abstract:
In this talk we give an overview on the metric aspect of noncommutative geometry, especially the metric interpretation of gauge fields via the process of {fluctuation of the metric}. Connes' distance formula associates to a gauge field on a bundle $P$ equipped with a connection $H$ a metric that coincides with the horizontal metric as soon as the holonomy is trivial. Otherwise we exhibit an elementary example on a $2$-torus in which the noncommutative metric $d$ is somehow more interesting than the horizontal one since $d$ preserves the $S^1$-structure of the fiber and also guarantees the smoothness of the length function at the cut-locus. In this sense the fiber appears as an object "smoother than a circle". As a consequence, from a intrinsic metric point of view any observer on the fiber can equally pretend to be "the center of the world".
Title: Quantum Symmetries of the $\mathcal{A}_{{4}}$\ Graphs of the DiFrancesco-Zuber System
Authors: D. Hammaoui and E. H. Tahri
Abstract:
This work is devoted to the study of quantum symmetries of the $\mathcal{A}_{4}$\ graphs of the $su(3)$ system in an algebraic point of view.\\{\it Proceedings of the international conference on high energy physics and mathematical physics, Marrakech march 2005.}
Keywords: CFT, fusion algebras, quantum symmetries and weak Hopf algebras.
observer on the fiber can equally pretend to be "the center of the world".
Title: On the Critical Space-Time Dimensions of Parasuperstrings
Authors: N. Belaloui and L. Khodja
Abstract:
We investigate the extension of the superstring theory in the formalism of the paraquantization. Unlike the quantum superstrings which are defined at space-time dimension D=10, in the case of the parasuperstrings, the four space-time dimensions D=3,4,6,10, (in which the classical superstrings can be formulated) survive. The consequences of this study on the heterotic parastrings is investigated, we found that in addition to the ordinary case (26,10) of the space-time dimensions in which the heterotic string can be formulated, in the case of the heterotic parastrings, only survives the case (14,6) which is based on the only possible group E8.
Title: On a Graded $q$-Differential Algebra
Authors: Viktor Abramov
Abstract:
We construct the structure of a graded $q$-differential algebra on a ${\bf Z}_N$-graded algebra by means of a graded $q$-commutator. We apply this construction to a reduced quantum plane and study the first order differential calculus on a reduced quantum plane induced by the $N$-differential of the graded $q$-differential algebra.
Title: Mott Scattering of Polarized Electrons in a Strong Laser Field
Authors: B. Manaut, S. Taj and Y. Attaourti
Abstract:
We present analytical and numerical results of the relativistic calculation of the transition matrix element $S_{fi}$ and differential cross sections for Mott scattering of initially polarized Dirac particles (electrons) in the presence of strong laser field with linear polarization. We use exact Dirac-Volkov wave functions to describe the dressed electrons and the collision process is treated in the first Born approximation. The influence of the laser field on the degree of polarization of the scattered electron is reported.
Title: Crosstalk and Energy Resolution Studies in the ATLAS Electromagnetic EndCap Calorimeter
Authors: A. Elkharrim, J. Derkaoui, F. Maaroufi and B. Dekhissi
Abstract:
ATLAS (A Toroidal LHC ApparatuS) is one of the experiments at the Large Hadron Collider (LHC) at CERN planned to be operational by the year 2007. The main goal of the experiment is the discovery of the Higgs boson, the missing piece in the Standard Model (SM) of Particle Physics and to explore physics beyond the SM. The accordion-shaped Electromagnetic Calorimeter End-Cap (EMEC) is one of the ATLAS sub-detectors designed to stop e+, e- and photons coming from the collision by forcing them to make an electromagnetic shower. One of the basic requirements set on the detector by the ATLAS physics is an excellent energy resolution over a wide energy range. As long as the energy measurements are closely linked to system electronics, the study of crosstalk signals appears to be necessary.
only survives the case (14,6) which is based on the only possible group E8.

Title: Corrélation entre des Mesures au Sol d'épaisseur Optique des Aérosols et des Mesures Satellitaires TOMS Earth Probe d'Indice en Aérosol sur la Région de Marrakech
Authors: A. Bounhir, E.A. Siher and Z. Benkhaldoun
Abstract:
Le but de ce travail est d'étudier la corrélation entre des mesures au sol d'épaisseur optique des aérosols et leurs indices mesurés par le satellite Earth Probe TOMS (Total Ozone Mapping Spectrometer). Les séries de mesures satellitaires concernent la région de Marrakech et le site des mesures au sol se trouve à 12 Km de la ville de Marrakech. De part sa position géographique, cette région est connue pour ses aérosols de type désertiques. Une corrélation satisfaisante a été établie entre l'indice en aérosol et l'épaisseur optique. Le facteur de corrélation dépasse les 80\%.

Title: The Search for High Energy Cosmic Rays Flux Variations in an underground Detector
Authors: A. Moussa, H. Dekhissi, F. Maaroufi, J. Derkaoui
Abstract:
We present the result of a search for muons flux variations. About 10 million high-energy muons, collected with the MACRO detector at the underground Gran Sasso Laboratory, have been used for this analysis. Two different analysis were used to search for the occurrence of clusters of events: time interval distribution and scan statistics. The results of our analyzes confirm with high statistics a random arrival time distribution of high energy cosmic rays (CR).