Group Members

Visitors:

Research visits of members of the group:

Guest professorship:

Research funds and support:

Lectures at Summer- or Winter-Schools, Organization of Workshops:

E. O. Alt: Lecture 'News in Charged-Composite Particle Scattering: Theory and Applications', [MZ-TH/02-19] XVIII. Eur. Conference on Few-Body Problems in Physics, Bled, Slovenia, September 2002.

J. Körner: Lectures on 'One-loop Corrections to Polarization Observables', International School on heavy particle physics, Dubna, Russia, 2002 and Klausurtagung des GK Mainz, Bullay, 2003;
Lectures on 'Angular Decay Distributions in Heavy Particle Decays', Helmholtz International School "Heavy Quark Physics", Dubna, Russia, 2005;
Lectures on 'Physics of Heavy Quarks', University of Pavia, Italy 2002.

M. Reuter: Lectures on 'Nonperturbative Quantum Gravity', School on Integrability in Quantum Field Theory and Quantum Statistics, Tbilisi, Georgia, 2002;
Lectures on 'Renormalization Group Methods', Saalburg Summer School for Graduate Students.

F. Scheck: Workshop "Renormalization and Regularization", Hesselberg 2002 (together with R. Nest, Kopenhagen and E. Vogt, Berlin).

S. Weinzierl: Lectures on 'Higher Order Perturbation Theory', Postgraduate AIO/OIO School, Nijmegen, January/February 2005;
Lectures on 'Symbolic Computations in C++ and Introduction to GiNaC', Computer Algebra and Particle Physics 2005, DESY Zeuthen, April 2005;
Coordination of a working group on 'Schleifenrechnungen zwischen Physik und Mathematik', Sommerakademie der Studienstiftung des deutschen Volkes, Görlitz, September 2005.

Introduction

The research of the group deals with various aspects of the fundamental interactions of nature and of the inner structure of elementary particles. It ranges from perturbative quantum field theory, as applied to hadron physics, within the framework of quantum chromodynamics, and to electroweak interactions of quarks and leptons, to extensions of Yang-Mills gauge theories within non-commutative geometry and nonperturbative quantum gravity. Research in phenomenological particle physics centers on perturbative quantum field theory at the level of two loops, on the physics of hadrons containing heavy quarks, and on the physics of charged leptons and their neutrinos. On a more theoretical side, it covers algebraic Yang-Mills-Higgs theories, and their quantization, as well as their application to particle physics. Further activities concern three-body problems in quantum physics, formal aspects of quantum perturbation theory, the inverse scattering problem, and impedance tomography.

A series of textbooks on theoretical physics (F. Scheck, Springer-Verlag) has been completed and revised editions appeared: the 7th edition of Theoretische Physik 1: "Mechanik - Von den Newtonschen Gesetzen zum deterministischen Chaos" appeared in 2003, Theoretische Physik 2: "Nichtrelativistische Quantentheorie: Vom Wasserstoffatom zu den Vielteilchensystemen" was completed in 2000, Theoretische Physik 3: "Klassische Feldtheorie - Von der Elektrodynamik zu den Eichtheorien" appeared in 2003, and Theoretische Physik 4: "Quantisierte Felder - Von den Symmetrien zur Quantenelektrodynamik" in 2001. The English translation of volume 1 "Mechanics - From Newton's Laws to Deterministic Chaos", experienced a fourth edition in 2004.

Research Projects

Algebraic and Geometrical Methods in Quantum Field Theories

1. Algebraic Yang-Mills-Higgs Theories and Applications (R. Häußling, F. Scheck et al.)

Extensions of Yang-Mills theories to algebraic Yang-Mills-Higgs theories based on Non-commutative Geometry are by now well established. These theories provide a geometric interpretation of spontaneous symmetry breaking and incorporate chiral fermions as dynamic building blocks. They achieve a novel unified description of electroweak, strong and gravitational interactions. Our group was the first in Germany who took up this field of research in the late 1980's and early 1990's and had an active share in its development. We have continued work on the model developed in Mainz and Marseille, especially focusing on the question of an adequate quantization of the model, taking into account the noncommutative structure seriously [MZ-TH/01-25] and its applications to particle physics.

2. Non-Commutative Geometry, Hopf Algebras and Fundamental Interactions (M. Paschke, F. Scheck, A. Sitarz et al.)

Connes' non-commutative geometry as applied to the physics of the standard model and to gravity raises important conceptual questions and gives strong hints at a better understanding of the role of quantum groups in physics. Specific issues dealt with in this context concern generalized differential calculi and connections the classification of finite Spectral Triples and their relation to Hopf algebras. Work is done also on finding and elaborating constructive examples within the spectral triple approach and in view of quantization [MZ-TH/99-53].

3. Spin-Statistics Relation and its Geometric Origin (N. Papadopoulos, M. Paschke, A. Reyes, F. Scheck)

The well-known theorem on the relation between the spin of identical particles and the statistics they obey, is proved in covariant, relativistic quantum field theory. The proof is based on Lorentz covariance and, in particular, on microcausality. Yet, the decisive phase (-)^2s, with s the spin, stems from the rotation group only. Therefore, the question arises whether the theorem holds also for ordinary (nonrelativistic) quantum mechanics, and if so, under which conditions. In our analysis [MZ-TH/04-24]. we concentrate on the geometrical and topological properties of the underlying configuration space and their relation to the Bose-Fermi alternative.

4. Algebraic Structures of Quantum Field Theories (D. Kreimer et al.)

The research is focused on the investigation of algebraic structures in renormalization theory and perturbative quantum field theory. In collaboration with Alain Connes (IHES and Collège de France, Paris) we achieved a reformulation of renormalization theory as a Riemann-Hilbert problem, with the splitting of an unrenormalized Green function into counterterms and finite renormalized quantities appearing as a corresponding Birkhoff decomposition, exhibiting sources of the rich analytic structure of QFT-relations to iterated integrals and shuffle algebras familiar in the theory of polylogarithms and zeta functions. Applications of these results led to high-order loop calculations in collaboration with David Broadhurst, allowing for tests of non-perturbative Borel resummation techniques, as well as to manifold connections to number theory. The detailed results obtained in 1998-1999 include a complete resolution of overlapping divergences in terms of the Hopf algebra of the classifying space of rooted trees and Feynman graphs, a classification of these Hopf algebras and an identification of the dual Lie algebras, including the relation to Hochschild cohomology. Finally, in a collaboration with E. Mielke (Mexico), chiral anomalies in space-times with torsion were studied, a topic which gave rise to controversial results in the literature due to an often erroneous use of renormalization prescriptions. [MZ-TH/98-19, 20, 31, 35, 39, 42, 43, 50, 99-14, 15, 38, 54, 55, 57].

5. Nonperturbative Renormalizability of Quantum Einstein Gravity (M. Reuter et al.)

Gravity is quantized using the method of the "effective average action", a scale dependent Wilson-type free energy functional whose scale dependence is governed by an exact renormalization group (RG) equation. It describes the RG flow on the infinite dimensional theory space consisting of all diffeomorphism-invariant action functionals which is caused by systematically increasing the wavelength of the quantum fluctuations integrated out. Nonperturbative solutions to the RG equation can be obtained analytically by projecting the RG flow onto a certain particularly important, finite dimensional "truncated" theory space. In particular within the Einstein-Hilbert-truncation, the beta-functions of Newton's constant and the cosmological constant were derived exactly [MZ-TH/00-56] and the resulting flow was determind numerically [MZ-TH/01-27]. On the formal side, an improved flow equation based upon the transverse-traceless decomposition of the metric has been introduced [MZ-TH/01-21], and it has been applied to a generalized truncation containing a term quadratic in the curvature [MZ-TH/02-07]. The reliability of this truncation has been tested by comparing it to the Einstein-Hilbert truncation, and by analyzing the cutoff-scheme dependence of universal quantities such as critical exponents. We find strong evidence supporting the conjecture that the ultraviolet behaviour of Quantum Einstein Gravity is governed by a non-Gaussian RG fixed point. If it exists, the theory is renormalizable at the nonperturbative level and likely to be consistent and predictive at arbitrarily small distances [MZ-TH/01-26, MZ-TH/01-38]. It is free from unphysical singularities then, or "asymptotically safe" in Weinberg's sense. The viability of this scenario has also been successfully tested using a proper time flow equation [MZ-TH/04-16], an approach somewhat less sophisticated than that of the effective average action.

6. Quantum Gravity Effects in Black Hole Spacetimes (M. Reuter et al.)

The results for the RG running of Newton's constant have been used in order to take the leading quantum corrections to the metric of black hole spacetimes into account. In particular, it has been argued [MZ-TH/00-04] that the Hawking evaporation of a Schwarzschild black hole stops once its mass is of the order of the Planck mass, and that the final state of the evaporation process is a cold, soliton-like remnant of Planckian dimensions. The structure of the Cauchy horizon singularity formed in a realistic gravitational collapse has also been studied [MZ-TH/98-45].

7. The Cosmology of the Planck Era (M. Reuter et al.)

The scale dependence of Newton's constant and the cosmological constant predicted by the RG equation of Quantum Einstein Gravity modifies the evolution of the Universe. In particular, the cosmology of the "Planck era" immediately after the initial singularity is governed by the ultraviolet fixed point [MZ-TH/01-18]. It is found that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problems of standard cosmology, and could generate a spectrum of primordial density fluctuations which is scale-free (spectral index n=1), at least at short wavelengths. While the first investigations of RG effects in the early universe were based upon an "RG-improvement" of the field equations, a more powerful approach, the RG-improvement of the underlying action functional was developed and applied to cosmology in [MZ-TH/03-20]. The resulting theory has certain features in common with Brans-Dicke Theory.

8. Infrared Properties of Quantum Einstein Gravity (M. Reuter et al.)

One of the notorious problems of Euclidean gravity is the conformal factor instability which means that the Einstein-Hilbert action is not positive definite and that flat space is not its global minimum. It is plausible to speculate that quantum gravity effects lead to a dynamical stabilization of the conformal factor. In order to get a first understanding of how this might happen a scalar toy model with a non-standard kinetic term has been analyzed in detail [MZ-TH/00-25]. Its (in)stability properties are similar to those of gravity theories with higher derivative actions.

Motivated by the conjecture that the cosmological constant problem is solved dynamically by strong quantum effects in the infrared, the RG equation of Quantum Einstein Gravity was used in order to perform a first analysis of the renormalization properties on nonlocal invariants [MZ-TH/02-09, 03-19]. It was found that, provided invariants of the type considered (nonlinear functions of the Euclidean spacetime volume) are actually generated by the RG flow, one can obtain very large, almost flat Universes without fine-tuning the (Planck-size) bare cosmological constant.

9. Fixed Point Cosmology of the Late Universe (M. Reuter et al.)

A conjecture has been formulated according to which at very large spacetime distances, too, Newton's constant and the cosmological constant are subject to strong renormalization effects due to a second RG fixed point which is infrared attractive. Within the phenomenological analysis performed, the microscopic origin of the RG running is irrelevant; it could be of a quantum mechanical, but also a completely classical nature. It was shown [MZ-TH/01-19] that this conjecture leads to a cosmology of the late (present) Universe with an accelerated expansion (q = - ¼) and a self-adjusting vacuum energy density which, for a spatially flat Universe, guarantees that both the matter and the vacuum energy density equal precisely one half of the critical density (Ω_M = Ω_Λ = 1/2). In view of the high-precision astronomical data which became available recently this is a very attractive scenario; it would provide a solution to the "cosmic coincidence puzzle" without invoking a quintessence field. In order to discuss structure formation in this "infrared fixed point cosmology", a gauge-invariant approach to the cosmological perturbation theory of Universes with time-dependent Newton and cosmological constant has been developed [MZ-TH/02-16]. The viability of the model was tested by comparing its prediction for the distance-redshift relation to the HzST and SCP data on high redshift supernovae of type Ia which are used as standard candles. It was found [MZ-TH/03-04] that the model reproduces the data even slightly better than the best-fit standard Friedmann-Robertson-Walker cosmology.

10. Galactic Dynamics without Dark Matter (M. Reuter et al.)

In refs. [MZ-TH/04-14, 04-15] arguments were presented which point in the direction that quantum gravity might imply macroscopic quantum effects which make their appearance at typical galactic scales. For a phemonological analysis the improved-action approach was used to investigate the relationship between the hypothetical scale dependence of Newton's constant and the galaxy rotation curves one would expect. It turned out that an extremely tiny distance dependence to Newton's constant is enough to produce the observed almost flat galaxy rotation curves without postulating any dark matter.

11. Quantum Gravity in Three Dimensions (H.-J. Matschull et al.)

From the mathematical point of view, Einstein's theory of gravity can be simplified considerably when space-time is assumed to be three dimensional. Based on this observation, simplified toy models can be constructed that describe the interaction of particles with the gravitational field, or the creation of black holes and wormholes. Some of these models can be solved completely both at the classical and at the quantum level. That is, the most general solution to the classical equations of motion can be given, and the quantum Hilbert space can be defined explicitly. Hence, a consistent quantum theory of gravity can be formulated, based on the basic principles of quantum physics and general relativity.

Some interesting physical effects, such as a certain non-commutative structure of space-time and a discretization of geometry, can be seen in these toy models, and it can be understood in detail how these effects arise from the underlying mathematical structures. It is expected that some of the features of the toy models will also arise in a fully consistent, four dimensional quantum theory of gravity, provided that such a theory exists. The results from our toy models are therefore useful to get some ideas of how such a theory may look like. We are currently working on a model describing the creation of a black hole [MZ-TH/99-17, 99-31, 00-44, 00-45].

12. Geometrical Methods in Classical and Elementary Particle Physics (M. Debert, A. Holfter, N. Papadopoulos, A. Reyes et al.)

The connection between classical physics and quantum physics is investigated. The most remarkable difference between quantum and classical physics is the fact that in quantum physics the interpretation is part of its formulation. This has important implications in many fundamental problems in elementary particle physics. It leads to investigations on quantization in various ways: within the framework of non-commutative geometry, deformation quantization, BRS formalism, quantum groups and Hopf algebras. In this connection the role of quantum groups as generalized symmetries in noncommutative geometry is investigated [MZ-TH/01-09]. Especially the quantum group structure which is associated with a noncommutative torus is found. This opens the possibility to discuss a whole class of quantum groups structures and to construct the corresponding models.

The question of quantization of spacetime within the framework of noncommutative geometry is investigated in [MZ-TH/01-35, 03-T2]. In this approach the path integral contains state sums of Dirac operators which correspond to all admissible spacetimes. This was done for the zero-dimensional case, i.e. for discrete spacetimes. The extension to higher dimensions is planned for future investigations.

Some elementary aspects of quantization are discussed in Quantized Free Fields (by A. Reyes, Hesselberg Meeting Theory of Renormalization and Regularization, February 2002.

Mixing of Weak Interaction States

13. Mass Matrices and Neutrino Oscillations (G. Barenboim, S. Falk, R. Häußling, F. Scheck)

The Cabibbo-Kobayashi-Maskawa mixing matrix for quarks and the analogous mixing matrix for neutrinos are manifestations of the mismatch between the mass eigenstates and the weak interaction states. After suitable redefinition of phases of the base states, they constitute an additional set of observables within the standard model whose dynamic origin is encoded in the mass matrices of quarks and leptons, respectively, with two charge sectors each. The latter, however, are ambiguous. Their reconstruction from the observed mixing [MZ-TH/02-02] has to cope with high-dimensional manifolds of choices and needs further physics input.

We have developed a simple, model-independent scheme that allows to reconstruct an effective mass matrix from the observable mixing matrix in a unique way. The latter is easily transformed, by means of correlated bi-unitary transformations in the two charge sectors, to any basis of chiral states, in view of making contact with individual model building. Our scheme also allows to introduce physical hypotheses about the origin of mass differences and of mixing in a transparent manner.

We showed that a consistent interpretation of all neutrino anomalies (including the LSND experiment) is achievable with three generations only, no sterile neutrino is needed [MZ-TH/98-29]. State mixing is found to be strong and to involve all three generations simultaneously. As a consequence, leptonic CP violation, if it is present, should be observable in neutrino beams from muon storage rings [MZ-TH/99-56]. Predictions for long-baseline oscillation experiments are worked out showing that a complete determination of the mixing matrix seems possible [MZ-TH/98-52]. It is also shown that the two squared mass differences of neutrinos can be obtained consistently from loop effects in left-right symmetric models, assuming primordial masses of neutrinos to vanish [MZ-TH/99-09]. Finally, investigation of hadronic CP violation within left-right symmetric models and of implications for baryogenesis and other phenomena was part of an ongoing research program with various scientists in Europe and the USA.

Few-Particle Scattering

14. Compactness of the Kernels of AGS Three-Body Momentum Space Integral Equations for Charged Particles (E. O. Alt et al.)

Modern analyses of few-particle reactions are successfully based on Faddeev or Alt-Grassberger-Sandhaas (AGS) momentum space integral equations. They are, however, valid only if the interparticle interactions are of short range since in the presence of long-range Coulomb interactions they loose their compactness property. For the AGS equations these problems have now been resolved. Indeed, if all Coulomb interactions are purely repulsive, suitably modified integral equations for the reaction amplitudes for all binary processes have been proven to possess compact kernels for all energies, thus rendering them amenable to standard solution methods [MZ-TH/99-62, MZ-TH/00-34]. This result supports the previously developed "screening and renormalization approach" (for a review see [MZ-TH/95-05] ).

15. Novel Approach to Scattering of Charged Composite Particles (E. O. Alt et al.)

Standard approaches to three-body scattering encounter typical difficulties as soon as charged particles are involved. They are caused by the long range of the Coulomb potentials, and result in either complicated asymptotic boundary conditions in coordinate space or in corresponding severe singularities in momentum space. Though, at least for purely repulsive Coulomb interactions all theoretical problems are solved by now (see project 11). But applications are very expensive and partly still involve approximations the consequences of which can not easily be quantified. As a further alternative we have developed a novel approach. It is based on constructing a unitary operator that transforms the three-body Hamiltonian into a simpler operator such that standard treatments are applicable. This goal is accomplished by means of an eigenfunction expansion that reflects the characteristic large-distance behavior of the Coulomb-like potentials acting between the charged particles. In a first step we consider the simplest case of a Hamiltonian containing short-range pair potentials, and a repulsive Coulomb potential between two particles only. The objective here is that by this unitary transformation the Coulomb potential is actually eliminated. Consequently, the transformed Hamiltonian is, indeed, simplified as it has become similar to that of a Hamiltonian without Coulomb potential [MZ-TH/02-33, 03-01, 03-12].

If the Coulomb potential is attractive, additional problems arise because the eigenfunction expansion mentioned above which is used for the construction of the unitary operator includes also the infinite number of eigenfunctions belonging to the discrete spectrum. Nevertheless, first results demonstrate that this concept can also be used for attractive Coulomb potentials [MZ-TH/02-11, 03-05].

In order to perform these investigations we had to develop an new integral representation of the two-body Coulomb scattering wave function in which the integration is to be performed on the real axis only (in contrast to the standard forms which contain contour integrations in the complex plane) [MZ-TH/01-30]. This representation might be of use also for other investigations.

16. Application of Three-Body Methods to Atomic Collisions (E. O. Alt et al.)

Many interesting atomic processes are of three-body type, an important example being direct scattering and charge transfer of electrons off hydrogenic atoms. Standard atomic methods are unable to describe simultaneously the direct and exchange processes, in part due to their neglect of unitarity and channel coupling. Based on three-body integral equations we have developed an approach, to be applied at higher energies, which takes into account the constraints of two- and (partly) of three-body unitarity and treats all the open channels on equal footing. This leads to a very satisfactory description, not only of total cross sections for the electron exchange reaction but also of differential cross sections for electron direct scattering and exchange in reactions with hydrogen atoms [E. O. Alt, A. S. Kadirov, and A. M. Mukhamedzhanov, Proton-Hydrogen Charge Exchange and Elastic Scattering in the Faddeev Approach: Asia Pacific Conference on Few-Body Problems in Physics, Noda/Kashiva (Japan), Conference Handbook, p. 127, and Few-Body Syst. Suppl. 12, 75 (2000); E. O. Alt, A. S. Kadirov, and A. M. Mukhamedzhanov, Importance of two-body Coulomb rescattering and cross-channel coupling in proton-hydrogen collisions: 16th Few-Body Conf, Taipei, 2000, Conference Handbook, pg. 429; Nucl. Phys. A684, 693c (2001); XVIIth Europ. Few-Body Conf, Evora, 2000, Conference Handbook, pg. 214; MZ-TH/00-35)]).

17. Coulomb Effects in Proton-Deuteron Scattering (E. O. Alt et al.)

Experimental and theoretical investigation of nucleon-deuteron scattering is of crucial importance as it is the simplest reaction which is sensitive to off-shell effects of the fundamental nucleon-nucleon interaction and to the equally fundamental three-nucleon forces. Experimentally most extensively studied is the reaction with protons as projectiles. Above the deuteron breakup threshold, the only approach mathematically proven to be rigorously valid is the "screening and renormalization approach" (see project 11). Based on it we have succeeded to perform calculations of pd elastic scattering observables for energies between 2.5 and 22.7 MeV with the realistic "Paris" NN potential. While experimental differential cross sections are well described, the well-known discrepancies between theory and experiment for polarization observables (``the A_y puzzle'') remain unexplained yet. [E.O. Alt, A.M. Mukhamedzhanov, A.I. Sattarov: The `Sagara discrepancy': fact or fiction?: 16th Few-Body Conf, Taipei, 2000, Conference Handbook, pg. 357; XVIIth Europ. Few-Body Conf, Evora,2000, Conference Handbook, pg. 66; Energy-dependence of proton-deuteron scattering observables: 16th Few-Body Conf, Taipei, 2000, Conference Handbook, pg. 355; Nucl. Phys. A684, 542c (2001); XVIIth Europ. Few-Body Conf, Evora, 2000, Conference Handbook, pg. 68; MZ-TH/01-24]. )

18. Post-Acceleration Effects in the Coulomb Breakup of Light Nuclei (E. O. Alt et al.)

Knowledge of the astrophysical S-factors for certain nuclear fusion reactions at extremely low energies is important as ingredient in stellar evolution models, for the estimation of the relative abundance of elements, of expected neutrino fluxes, etc. Besides direct measurements which are greatly suppressed by the Coulomb barrier between the fusing nuclei at the required low energies, experiments on the inverse process, namely the Coulomb breakup in the field of a heavy, fully stripped nucleus, are being performed. However, in order to extract the S-factor from such reactions it must be taken into account that the nucleus not only serves as a source of photons to induce the breakup of the projectile, but also influences the ejectiles afterwards (Post Coulomb Acceleration effect, PCA). Theoretical treatments of PCA effects require knowledge of the three-charged particle wave function in the appropriate asymptotic regions (see E. O. Alt and A. M. Mukhamedzhanov, On the asymptotic solution of the Schrödinger equation for three charged particles: Phys. Rev. A 47 (1993) 2004) and, therefore, have generally been ignored up to now. Investigations of the influence of PCA on the 7Be(p,gamma)8B breakup reaction in the Coulomb field of a fully stripped lead nucleus which determines the high energy neutrino flux from the sun have been performed and the influence on the value of the extracted S-factor has been estimated [E.O. Alt, B.F. Irgaziev, A.M. Mukhamedzhanov, and A.T. Muminov, Final state three-body Coulomb effects in the ²⁰⁸Pb(⁸B, ⁷Be p)²⁰⁸Pb Coulomb breakup: XVIIth Europ. Few-Body Conf, Evora, 2000, Conference Handbook, pg. 248; MZ-TH/02-17, 03-02, 03-07]. See also [MZ-TH/03-13, 04-10, 04-13].

19. Coulomb Corrections in High-Energy Heavy Ion Collisions (E. O. Alt et al.)

High-energy heavy ion collisions provide an important tool for proving the existence, and studying the properties, of the quark-gluon plasma. In particular Hanbury-Brown Twiss (HBT) interferometry allows to draw conclusions on the evolving space-time geometry of the interaction region. For the interpretation of the HBT results the Coulomb interaction between the detected particles must be taken into account in a detailed manner. We have derived a systematic procedure for dealing with Coulomb effects in three-body correlation functions which greatly improves upon the standard (but only phenomenological) "Gamov factor approximation" [E.O. Alt, T. Csörgö, B. Lörstad, J. Schmidt-Sørensen, Eur. Phys. J. C 13, 663 (2000); MZ-TH/01-07].

20. Mesomolecules (E. O. Alt et al.)

Calculation of the energy levels of antiprotonic (or mesonic) atoms represents a great computational challenge as masses, as well as length scales, which differ by several orders of magnitudes are involved. In addition, in the case of, e.g., antiprotonic atoms the absorption of the antiprotons occurs from states with large values of the orbital angular momentum L so that only transitions between states with large L can be observed. Standard adiabatic approaches treat the rotational motion perturbatively and hence are not well suited to treat such highly rotationally excited systems. We have developed a new hyperradial adiabatic approach which is applicable to Coulombic three-body systems irrespective of the masses of the constituents and in which systems with large total angular momentum J are not more difficult to treat than those with low J [A. V. Matveenko and E. O. Alt, Novel approach to highly rotational states of atomic molecules: 16th Few-Body Conf, Taipei, 2000, Conference Handbook, pg. 434; A. V. Matveenko and E. O. Alt, Semianalytic wave functions for highly rotational states of antiprotonic He: Hyperfine Interactions 127 (2000) 143; MZ-TH/00-19; A. V. Matveenko and E. O. Alt, Rotational Three-Body Resonances: A New Adiabatic Approach, Few-Body Syst. Suppl. 13, 140 (2001)]. First numerical applications have already been performed for the interesting problem of rotationally excited states of the He4-trimer, proving that the existence of such states can definitely be excluded [MZ-TH/01-17, MZ-TH/02-12, MZ-TH/02-18]. A program for calculating abscissas and weights of Gaussian quadrature rule for arbitrary weight functions and intervals which can be applied in the Coulombic three-body problem was developed in [MZ-TH/04-09, 04-11, 04-12].

Strong Interactions at Low Energies

21. Extraction of Low Energy QCD Parameters from tau-Decay (K. Schilcher et al.)

With the advent of precise measurements of the vector (V) and axial-vector (A) spectral functions, obtained from tau-lepton decay, an opportunity was opened to check the precision of the QCD sum rules in the light-quark sector of QCD and simultaneouly extract some fundamental parameters of QCD. The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data. The sum rules exhibit poor saturation up to current energies just below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is generalized to determine the value of the finite remainder of the (V-A) correlator, and its first derivative, at zero momentum: Π(0) = - 4L₁₀ = 0.0257 ± 0.0003, and Π'(0) = 0.065 ± 0.007 GeV^-2. These parameters are related to the O(p⁴) and O(p⁶) counter terms of chiral perturbation theory. The dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion are also determined: O₆ = - (0.004 ± 0.001) GeV⁶, and O₈ = -(0.001 ± 0.006) GeV⁸ [MZ-TH/03-16]
A completely different approach based on a functional method was used in MZ-TH/03-21 to compare the time-like τ-data with the asymptotic space-like QCD results. This method is more general than other approaches, however, the increased credibility has to be paid by larger errors for the extracted parameters. Numerical results were obtained for O₆^V-A and support the validity of the sum rule results.

22. Determination of the Charm-Quark Mass (J. Bordes, J. Peñarrocha and K. Schilcher)

A precise determination of the strange-quark mass is of crucial importance to pin down the fundamental parameters of the standard model. A new determination of the charm-quark mass was carried out using QCD finite energy sum rules for positive moments of the total e⁺e^- cross section. As phenomenological input we use the new and superior BESII data. As theoretical input we employ new QCD results to O(α_s²) and O(m_c¹²/q¹²) in combination with the method of analytic extrapolation by duality developed in Mainz. We obtain the result: m_c(m_c) =(1.37 ± 0.09) GeV, [MZ-TH/01-12] in agreement with conventional determinations based on inverse moment sum rules. By the same method we have also determined the mass of the bottom quark [MZ-TH/02-31]. This parameter is phenomenologically of special importance, as it is required for the interpretation of most of the exciting new results emerging from the B-factories. This research was carried out in a collaboration with scientists from the university of Valencia, the partner university of Mainz.

23. Delta I=1/2 Enhancement and the Glashow-Schnitzer-Weinberg Sum Rule (K. Schilcher, N. F. Nasrallah)

In 1967 Glashow, Schnitzer and Weinberg derived a sum rule in the soft-pion and soft-kaon limit relating the Delta I=1/2 non-leptonic K → 2 π amplitude to integrals over strange and non-strange spectral functions. Using the recent ALEPH data from tau-decay, we show that the sum rule, slightly modified to reduce contributions near the cut, yields the correct magnitude of the decay amplitude corresponding to the Delta I=1/2 rule [MZ-TH/00-02].

24. Is There Evidence for Dimension-Two Corrections in QCD Two-Point Functions? (K. Schilcher, C. A. Dominguez)

The ALEPH data on the (non-strange) vector and axial-vector spectral functions, extracted from tau-lepton decays, is used in order to search for evidence for a dimension-two contribution, C_{2 V,A} to the operator product expansion (other than d=2 quark mass terms). This is done by means of a dimension-two finite energy sum rule, which relates QCD to the experimental hadronic information. The average C₂ = (C_2V + C_2A)/2 is remarkably stable against variations in the continuum threshold, but depends rather strongly on Λ_QCD. Given the current wide spread in the values of Λ_QCD as extracted from different experiments, we would conservatively conclude from our analysis that C₂ is consistent with zero [MZ-TH/99-08].

25. Two-Loop Calculations in Chiral Perturbation Theory (P. Post, K. Schilcher)

Recent progress in the calculation of massive Feynman integrals allows phenomenological studies of physical amplitudes to an accuracy in unison with the high precision of existing or planned experiments. Results of the two-loop calculation in full SU(3) × SU(3) chiral perturbation theory are obtained for a specific linear combination of weak and electromagnetic form factors (the one appearing in Sirlin's theorem) which does not receive contributions from O(p⁶) operators with unknown constants. For the charge radii, the corrections to the previous one-loop result turn out to be significant. To clearly identify the two-loop effects, more accurate measurements of the kaon electromagnetic and weak charge radii would be desirable. The question of convergence of the chiral expansion is addressed [MZ-TH/97-02]. The electromagnetic form factor of the neutral kaon is calculated in O(p⁶) chiral perturbation theory. At O(p⁶), a new operator enters whose arbitrary renormalization constant, however, results only in a parallel shift in the form factor F(t)/t. The two-loop effects are non-negligible, but comparison with experiment would require higher precision data [MZ-TH/00-31]. Finally all electromagnetic and semi-leptonic form factors of pions and kaons were calculated in the same order. While the charge radii are related to free renormalization parameters, the q⁴-Term in the expansion of the semi-leptonic form factors of the kaon is predicted [MZ-TH/01-39]. This result should help in the interpretation of data from ongoing high precision experiments.

26. B and B_s Decay Constants from QCD Duality at Three Loops (J. Bordes, J. Peñarrocha and K. Schilcher et al.)

Using special linear combinations of finite energy sum rules which minimize the contribution of the unknown continuum spectral function, we compute the decay constants of the pseudoscalar mesons B and B_s. In the computation, we empoy the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running bottom quark mass. The sum rules show remarkable stability over a wide range of the upper limit of the finite energy integration. We obtain the following results for the pseudoscalar decay constants: f_B = 176 ± 5 MeV and f_Bs = 190 ± 24 MeV. The results are somewhat lower than recent predictions based on Borel transform, lattice computations or HQET. Our sum rule approach of exploiting QCD quark hadron duality differs significantly from the usual ones, and we believe that the errors due to theoretical uncertainties are smaller.

These decay constants are of great phenomenological interest since they enter in the input to non-leptonic B-decays, in the hadronic matrix elements of BBbar-mixing and in the extraction of |V_cb| from the leptonic decay widths of B-Mesons. Knowledge of the decay constants allows to estimate the so-called hadronic B parameter which is directly related to the deviation of the vacuum saturation hypothesis. The decay constants are therefore of central interest to the ongoing experiments carried out in B-factories. Unfortunately these matrix elements could not be measured directly so far, so that we have to rely on theoretical calculations [MZ-TH/04-18].

27. D and D_s Decay Constants from QCD Duality at Three Loops (J. Bordes, J. Peñarrocha and K. Schilcher et al.)

We compute the decay constants of the pseudoscalar mesons D and D_s using a linear combination of finite energy sum rules which minimize the contribution of the unknown continuum spectral function. We employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running charm quark mass. The theoretical uncertainties arising from the QCD asymptotic expansion are quite relevant in this case due to the relative small scale of the charm mass. We obtain the following results: f_D = 177 ± 21 MeV and f_Ds = 205 ± 22 MeV. These results, within the error bars, are in good agreement with estimates obtained using Borel transform QCD sum rules, but somewhat smaller than results of recent lattice computations [MZ-TH/05-12].

Phenomenology of Strong and Electroweak Interactions: Higher-Order Corrections

28. Higher-Order Corrections, Phenomenology of Collider Experiments (S. Weinzierl et al.)

The research in the phenomenology of elementary particles is centered around the calculation of higher-order corrections in perturbation theory, with a main focus on high-energy collider experiments (Tevatron, LHC, ILC [MZ-TH/04-19]). This involves setting up computer programs for the simulation of high-energy experiments, which are accurate up to the second or third order in the perturbative expansion. An example are two recent publications on the automatization of NLO calculations [MZ-TH/05-03, MZ-TH/05-22].

As many of the calculations alluded to above are rather lengthy, computer algebra has become an indispensable tool. Even worse, many of the commercial products are not able to process the amount of data required by state-of-the-art loop calculations. Therefore dedicated computer algebra systems have been developed, tailored to the needs of the high-energy-physics community. One example is the computer algebra system "GiNaC", developed at the University of Mainz. Current research adds additional functionality to this system, as for example in [MZ-TH/04-17].

Research in mathematical physics involves a few specific topics: First of all, one topic is given by multiple polylogarithms. These functions occur naturally in the results of loop calculations. Interestingly, they have a rich mathematical structure, for example they form Hopf algebras [MZ-TH/04-17]. Secondly, and not directly connected with the first topic, are new developments for the calculation of scattering amplitudes in gauge theories. In particular "maximal-helicity-violating vertices" have obtained a significant interest of the community in the past year. In our group we considered the extension of these techniques to massive quarks [MZ-TH/05-05, MZ-TH/05-21].

29. Top Quark Physics at Linear Colliders (C. Schwinn)

The large mass of the top quark motivates models where it plays a special role in electroweak symmetry breaking. Therefore it is important to determine the top quark couplings at future collider experiments in order to distinguish the minimal standard model from one of its extensions. At an international linear collider (ILC) the CKM matrix element V_tb can be measured in single top production e⁺ e^- → e^- ν_μ t bbar while the Yukawa coupling of the top quark to the Higgs boson can be measured in associated top Higgs production e⁺ e^- → t tbar H.

The physical final state for single top production consists of six fermions, with background contributions from top-pair production and vector boson fusion. The final state for associated top-Higgs production consists of eight-fermions with backgrounds from associated top-Z production and gluon-splitting to bottom quarks. In [MZ-TH-04-21] the relevant tree level cross sections have been calculated using the program package O'Mega/Whizard.

A consistent treatment of finite width effects has been essential in obtaining numerically reliable predictions. Several schemes for the treatment of the decay width of the top quark and the vector bosons have been implemented into O'Mega and compared numerically in the process of single-top production .

30. Massive Two-Loop Integrals (J. Körner, D. Kreimer, K. Schilcher, H. Spiesberger, S. Weinzierl, et al.)

Massive multi-loop Feynman diagrams are becoming increasingly important in the precision analysis of experimental data in the framework of the Standard Model. In a long-term project our group is involved in the automatic evaluation of massive multi-loop Feynman diagrams (called XLOOPS). A general review of the XLOOPS program and the integration techniques that go into XLOOPS was given some time ago [MZ-TH/97-32] (see also [MZ-TH/98-18]). XLOOPS aims to do as many of the necessary multi-loop integrations in closed form as possible and, if necessary, to provide efficient numerical codes to do the remaining integrations numerically. Many results described in other sections of this report will eventually contribute to the XLOOPS project (see e.g. sections 25, 28, 31, 32, 37). Most of recent improvements have been obtained in doctoral theses [MZ-TH/00-D2, 00-T2, 02-T2, 03-T1, 04-T1].

Previous versions of the XLOOPS programs had been written with the help of the computer algebra system Maple. It turned out that this (and other) commercial programming systems do not suit the needs for a large-scale project like XLOOPS. Therefore, C. Bauer, A. Frink and R. Kreckel developed a C++ library to replace Maple. Its name 'GiNaC' is an iterated and recursive acronym for 'GiNaC is Not a CAS', where CAS stands for Computer Algebra System. It is designed to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science (like computation-intense numeric applications, graphical interfaces, etc.) under one roof. It is distributed under the terms and conditions of the GNU general public license. The GiNaC homepage offers the programs and its full documentation, including a tutorial.

Previous related publications are [MZ-TH/00-17, 00-58, 01-02, 01-33, 02-01, 02-04].

31. QCD Radiative Corrections (J. Körner, Z. Merebashvili, M. Rogal)

In [MZ-TH/02-10] we calculated the one-loop amplitudes for the processes g+g → Q+Qbar and q+qbar → Q+Qbar. These are needed for the NLO calculation of heavy hadron production in hadronic collisions when spin effects are taken into account. In [MZ-TH/04-04, 04-20, 04-22] the one-loop calculation was extended up to the ε² contributions, where ε is the dimensional parameter. This extension will be needed in the so-called loop-by-loop contributions to a NNLO calculation of heavy hadron production.

32. Sunrise Topologies (J. Körner, S. Groote, A. Pivovarov)

There is a special class of multi-loop topologies, the so-called general sunrise topology, which can be calculated to any loop order using configuration space techniques. In a continuing investigation of these topologies we presented results on the Laurent series expansion in ε of general sunrise topologies with various mass configurations [MZ-TH/04-03]. In [MZ-TH/03-10] one of us gave an overview of techniques and results of the configuration space approach to the calculation of general sunrise topologies.

33. Radiative Corrections to Heavy Quark and Heavy Lepton Decays (J. Körner, M. Mauser, S. Groote, M. Fischer, H. S. Do)

In this set of papers we calculated the NLO corrections to polarization observables in heavy quark and heavy lepton decays. In [MZ-TH/01-03] we determined the strong and electroweak radiative corrections to the decay of an unpolarized top quark into a bottom quark and transverse and longitudinal W bosons. The techniques developed in this calculation could be applied to a determination of the O(α_s) correction of the semi-inclusive decays Λ_b → X_c + D_s (D_s^*) including Λ_b and D_s^* polarization effects [MZ-TH/03-06]. At the one-loop level the QCD and QED radiative corrections are quite similar so that the techniques developed in the previous QCD calculations could be gainfully employed to calculate the complete one-loop radiative QED corrections to the semileptonic μ- and τ-decays including the complete set of polarization observables [MZ-TH/02-03, 04-02]. In certain variants of the minimal Standard Model as in the the Two-Higgs-Doublet Model or in the supersymmetric MSSM one also has a charged Higgs boson H^± which could e.g. be seen in the decay t → b + H⁺. We determined the NLO radiative corrections to this decay including polarization effects for the top quark [MZ-TH/02-06, 02-14]. All our results on the one-loop corrections to polarization observables were reviewed in [MZ-TH/03-09].

34. Heavy Baryon and Meson Transitions in a Covariant Quark Model Approach (J. Körner, M. A. Ivanov et al.)

We used our previously developed fully relativistic quark model to determine the rates of the decays of different heavy baryons and mesons. In [MZ-TH/01-20] we studied the semileptonic decays of the lowest lying double heavy baryons. In [MZ-TH/02-34] we calculated the nonleptonic decays B_c → D_s + and B_c → D_s + D₀. We substantiated previous suggestions that these decays would be ideally suited for an extraction of the CKM angle γ. The paper [MZ-TH/02-35] is devoted to an analysis of the rare decays B → K + l + lbar and B_c → D(D^*) + l + lbar with special emphasis on the polarization obsevables that can be measured in these processes. In [MZ-TH/03-22] we applied the covariant quark model to a calculation of the cross sections of the charm dissociation processes J/Ψ + π → D(D^*) + Dbar (D^*bar) which are needed in the interpretation of J/Ψ rate suppression in heavy ion collisions.

35. Spectral Functions and QCD Sum Rules (J. Körner, A. A. Pivovarov, S. Groote et al.)

The spectral functions related to current correlators and moments of these are fundamental inputs in the QCD sum rule analyses of various physical processes. The papers [MZ-TH/01-06, 01-10] determine the low-energy gluon contributions to the electromagnetic current correlators of heavy quark currents. In [MZ-TH/01-15] we discuss the choice of weight functions for the spectral density of two-point correlators of hadronic currents over a finite energy interval. The electromagnetic current correlators figure prominently in the theoretical description of the hadronic contributions to the anomalous magnetic moment of the muon. The hadronic contributions to the anomalous magnetic moment of the muon were analyzed in depths in [MZ-TH/01-28, 01-31, 03-14]. The paper [MZ-TH/02-32] determines the so-called light-by-light scattering contribution to the anomalous magnetic moment of the muon in terms of fermionic and scalar bosonic loops. A detailed sum rule analysis of data on semileptonic τ-decays led to an improved determination of the strong coupling constant and the strange quark mass [MZ-TH/01-34, 02-26]. An overview of these studies was given in [MZ-TH/01-13]. [MZ-TH/03-08] contains a three-loop calculation of the mixing matrix element in the framework of QCD sum rules for three point functions. A review of the electron-positron annihilation cross section as a tool for high precision tests of the Standard Model was given in [MZ-TH/02-30]. NLO predictions for polarization effects in the electron-positron annihilation cross section were reviewed in [MZ-TH/02-29]. [MZ-TH/02-25] contains a NLO analysis of initial state polarization effects in e⁺-e^--annihilation into top quark pairs from threshold to ultrahigh energies. The report [MZ-TH/01-29] takes a more detailed look at the threshold region in the same process using the framework of nonrelativistic QCD. The QCD sum rule approach was also applied to an improved NLO determination of the mass of the exotic 1^-+ light hybrid meson [MZ-TH/02-36] which was taken to be a + g state. A mass value of around 1.6 GeV seems to be favoured by the sum rule approach. This result was corrobarated by the analysis in [MZ-TH/02-27] where a detailed SU(3) study of the decay of the exotic π₁(1600) meson state (with J^PC quantum numbers 1^-+) into a p-wave η' + π system revealed that this exotic meson is likely to be a member of a flavour SU(3) octet. Contrary to this, the SU(3) analysis of the decay of the exotic π₁(1400) into η+π leads to the conclusion that the π₁(1400) must be a + four-quark state belonging to the 10 + 10bar representation of SU(3). The QCD sum rule approach can also be used in the framework of the Heavy Quark Effective Theory (HQET). HQET sum rules were applied in [MZ-TH/01-37] to determine the lifetime of the heavy baryon Λ_b including 1/m_b² effects.

36. Light Cone Sum Rules (B. Melic, S. Prelovsek et al.)

The modern approaches to heavy-to-light nonleptonic decays of heavy mesons rely on light-cone distribution amplitudes of heavy and light mesons which enter and can be determined through light-cone sum rules. In [MZ-TH/02-08] we analyzed HQET light-cone sum rules including 1/m_Q corrections for the B → π transition. Various technical issues related to the scale dependence of the pion transition form factor were discussed in [MZ-TH/01-42, 01-43, 02-21]. In particular, the analysis led to a prescription of how to fix the BLM factorization scale in the transition form factor. [MZ-TH/02-24] contains a detailed NNLO analysis for the photon-to-pion transition form factor. The method of QCD light-cone sum rules was used in [MZ-TH/02-20, 02-22, 02-23] to calculate exclusive nonleptonic B-decays and to analyze the role of the nonfactorizable contributions in these decays. This mainly concerns the decays B → J/Ψ + K and B → π + π.

37. Hadronic Corrections at O(α²) to the Energy Spectrum of μ-Decay (A. Davydychev, K. Schilcher, H. Spiesberger)

A meaningful interpretation of high-precision measurements at LEP requires correspondingly precise theoretical predictions for the μ-decay constant G_μ. Two-loop corrections to G_μ are partly known since several years and complete calculations are of high topicality in present research. However, also the μ-decay spectrum is a high precision measurement. In [MZ-TH/00-46, MZ-TH/01-40] we have calculated a small, however important, subset of two-loop corrections described by Feynman diagrams with an internal quark and lepton loops using a dispersion relation technique. The spectrum is corrected by a smooth energy-dependent function.

38. Isolated Photons in Deep Inelastic Electron Proton Scattering (H. Spiesberger et al.)

With increasing luminosity at the HERA electron proton collider, experimental studies of the final states in deep inelastic scattering has become more and more feasible. The production of an isolated photon accompanied by a number of jets is one example. With QCD corrections at order O(α_s) available from our previous calculations this process can be used for meaningful tests of QCD. In [MZ-TH/00-06, MZ-TH/00-26] we included in a theoretically consistent way the contributions from quark-to-photon fragmentation. The results have been used now for direct comparisons to data by the experimental groups at HERA.

39. Inclusive Charmed Meson Production at Next-to-Leading Order QCD (H. Spiesberger et al.)

The production of charmed mesons (like D^* or D^±) has attracted a lot of interest in the past few years. Experimental data exist from photon-photon collisions, from photoproduction and deep inelastic ep scattering, and from the hadron collider Tevatron. Many of the data could not be described by previous QCD calculations which predicted too small rates. In perturbative QCD, the production of charmed mesons is related to the production of charmed quarks folded with fragmentation functions which describe the non-perturbative transition from quarks to hadrons. Starting with photon-photon collisions, we initiated a project to calculate the production of charm quarks including in a consistent way the finite mass of the heavy quark [MZ-TH/01-23, 03-03, 03-15]. Technically, the problem is to implement a consistent prescription for the subtraction of divergences form the hard scattering cross sections so that this prescription matches the definition of the fragmentation functions. The method has been extended and applied to photoproduction [MZ-TH/03-18] and to proton anti-proton collisions [MZ-TH/04-07]. Comparisons with more recent data show much better agreement between experimental observations and the new QCD predictions.

Phenomenology of New Physics

40. Physics Beyond the Standard Model in Electron Proton Scattering and e⁺e^- Annihilation (H. Spiesberger et al.)

In 1997, experiments at the electron-proton collider HERA have found an excess in the number of deep inelastic scattering events at highest momentum transfers. In addition, more events with high-energetic muons in the final state than expected were observed. This raised speculations about physics beyond the Standard Model. In a series of papers we explored possible explanations within and beyond the Standard Model for these experimental observations [MZ-TH/00-27, MZ-TH/01-22]

41. Electroweak Symmetry Breaking without Higgs Boson (C. Schwinn)

Theories with additional space dimensions offer new possibilities for gauge symmetry breaking by imposing boundary conditions on the gauge fields. Recently this mechanism has been used to construct models of Higgsless electroweak symmetry breaking in five space-time dimensions. In these models tree level unitarity in gauge boson scattering is restored by the exchange of gauge boson Kaluza-Klein modes instead of a Higgs boson.

In [MZ-TH-03-17] BRST symmetry has been used to verify the consistency of symmetry breaking by boundary conditions with the unitarity cancellations required in Higgsless models. Unitarity of scattering amplitudes involving top quarks in Higgsless models requires also the Kaluza-Klein modes of the third family quarks. In [MZ-TH-04-01] it has been shown that the relevant unitarity cancellations are consistent with the mechanism of fermion mass generation by gauge invariant boundary localized terms used in such models.

In [MZ-TH-05-07] these results have been used to constrain the couplings of the top quark to Kaluza-Klein modes and to derive implications for collider phenomenology. The results of this work have been summarized in [MZ-TH-05-20].

42. Consistent Treatment of the Higgs Boson Decay Width (C. Schwinn)

Calculations of cross sections involving unstable particles require a careful treatment of the decay widths. The usual Dyson summation of the self-energies mixes different orders of perturbation theory while gauge invariance and the resulting Ward identities and the Goldstone boson equivalence theorem hold order by order in perturbation theory. For the case of the Higgs resonance, this problem has been investigated in [MZ-TH-04-06] in the context of a collaboration with Thorsten Ohl (Univ. Würzburg) and David Ondreka (TU Darmstadt) on the construction of gauge invariant classes of Feynman diagrams.

In [MZ-TH-04-06] it has been shown that in a nonlinear parameterization of the Higgs sector of the minimal standard model, the Dyson-summation of the Higgs propagator is consistent with gauge invariance, in contrast to linear parameterizations. This is in agreement with an earlier conjecture of Valencia and Willenbrock. In a nonlinear parameterization of a 2-Higgs doublet model, the consistent Dyson summation is possible for all neutral Higgs bosons, but not for the charged scalars.

43. Supersymmetry Breaking (J. Körner, Chun Liu)

In [MZ-TH/02-15] we constructed a supersymmetric model with two copies of the Standard Model gauge group in the gauge mediated supersymmetry breaking scenario. The Standard Model is obtained after a first step gauge symmetry breaking.

Electrical Impedance Tomography (EIT)

44. Electrical Impedance Tomography (EIT) (C. Lehmann, M. Azzouz, K. Schilcher et al.)

EIT is an imaging technique of medical diagnostics, in which one tries to obtain information on the conductivity distribution in the interior of a body by measuring currents and voltages at the surface of the body. If successfully implemented, EIT would provide a non-invasive complementary alternative to more conventional imaging techniques. We have built an electrical impedance tomograph which makes it possible to reconstruct impedance distributions in the interior of a cylinder by means of measurements of currents and potentials on its boundary. The reconstruction algorithm is based on Newton's algorithm for the solution of non-linear integral equations, where the electric fields are calculated by the methods of finite elements and finite integrals and Green functions. The results can be represented graphically on a PC. The resolution is fine enough to envisage applications in medical diagnostics such as Mammography. Most previous EIT algorithms use two-dimensional models for the conductivity. Since the electric current does not flow in straight lines, this approximation seems to be unwarranted. We investigate a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the geometry of the measuring chamber and by restricting the nature of the object to be imaged and the information required from the image. In particular we seek to establish the existence or non-existence of a single object (or a small number of objects) in a homogeneous background and the location of the former in the (x,y)-plane defined by the measuring electrodes . Given in addition the conductivity of the object rough estimates of its position along the z-axis may be obtained [MZ-TH/00-54].

Scientific Papers, Publications and Conference Contributions

Theses

Doctoral Theses

00-T1

"Die Mammographie als Anwendungsbeispiel der elektrischen Impedanztomographie"
("Mammography as an example of application of the electrical impedance tomography"), [ps.gz],
Carsten Lehmann (2000),
supervisor: K. Schilcher

00-T2

"Computer-algebraische und analytische Methoden zur Berechnung von Vertexfunktionen im Standardmodell"
("Computer algebraic and analytical methods for the calculation of vertex functions in the standard model"), [ps.gz],
Alexander Frink (April 2000),
supervisor: D. Kreimer

00-T3

"Strahlungskorrekturen zu Polarisationsobservablen schwerer Quarks"
("Radiative corrections to polarization observables of heavy quarks"), [ps.gz],
Alfonso Leyva (December 2000),
supervisor: J. Körner

00-T4

"Die Rolle von Hopfkategorien und Operaden in störungstheoretischen Quantenfeldtheorien"
("The role of Hopf categories and operades in perturbative quantum field theories"), [ps.gz],
Mathias Mertens (December 2000),
supervisor: D. Kreimer

01-T1

"Polarisationseffekte in semileptonischen Zerfällen schwerer Quarks"
("Polarisation effects in semi-leptonic decays of heavy quarks"), [ps.gz],
Marcus Mauser (May 2001),
supervisor: J. Körner

01-T2

"Von Nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik"
("On non-commutative geometries, their symmetries, and a bit of high energy physics"), [ps.gz],
Mario Paschke (August 2001),
supervisor: F. Scheck

02-T1

"Ein, zwei Punkte zu Nichtkommutativer Geometrie und Quantenfeldtheorie auf diskreten Räumen", [ps.gz],
Christian Pöselt (March 2002),
supervisor: F. Scheck

02-T2

"Algorithmische Methoden zur Berechnung von Vierbeinfunktionen"
("Algorithmic Methods for Computing Four-Leg Functions"), [ps.gz],
Richard Kreckel (April 2002),
supervisor: K. Schilcher

02-T3

"Untersuchungen zum nichtstörungstheoretischen Renormierungsverhalten der Quanten-Einstein-Gravitation"
("Nonperturbative renormalization behavior of Quantum-Einstein-Gravity"), [ps.gz],
Oliver Lauscher (September 2002),
supervisor: M. Reuter

03-T1

"Feynman loop integrals and their automatic computer-aided evaluation", [pdf],
Do Hoang Son (August 2003)
supervisor: J. Körner

03-T2

"Nichtkommutative Geometrie und Quantisierung von Raumzeiten und Konfigurationsrämen", [ps.gz],
Alexander Holfter (Dezember 2003)
supervisor: N. Papadopoulos

04-T1

"Use of Computer Algebra in the Calculation of Feynman Diagrams", [pdf],
Christian Bauer (November 2004)
supervisor: K. Schilcher

Diploma Theses

00-D1

"QCD-Bestimmung des hadronischen Beitrags zum anomalen magnetischen Moment des Myons"
("QCD determination of the hadronic contribution to the anomalous magnetic moment of the muon"), [ps.gz],
Jochen Maul (March 2000),
supervisor: J. Körner

00-D2

"Der xloops-Algorithmus zur Berechnung von Feynman-Graphen in C++"
("The xloops algorithm for the computation of Feynman graphs in C++"), [ps.gz],
Christian Bauer (July 2000),
supervisor: K. Schilcher

00-D3

"QCD-Analyse von hadronischen τ-Lepton-Zerfällen"
("QCD analysis of hadronic τ lepton decays"), [ps.gz],
Florian Krajewski (June 2000),
supervisor: J. Körner

00-D4

"Die Riemannsche ζ-Funktion in iterierten Einschleifenintegralen"
("The Riemann ζ function in iterated one-loop integrals"), [ps.gz],
Isabella Bierenbaum (June 2000),
supervisor: D. Kreimer

00-D5

"Berechnungen zum radiativen Myonzerfall"
("Calculations of radiative muon decay"), [ps.gz],
Markus Lippert (December 2000),
supervisor: K. Schilcher

01-D1

"Renormierungsgruppenfluss der Quanten-Einstein-Gravitation in der Einstein-Hilbert-Trunkierung und nichtlokalen Erweiterungen", [ps.gz],
Frank Saueressig (November 2001),
supervisor: M. Reuter

01-D2

"Flavourmischungen und Rekonstruktion von Massenmatrizen"
("Flavour mixing and reconstruction of mass matrices"), [ps.gz],
Silke Falk (November 2001),
supervisor: F. Scheck

02-D1

"Beiträge neuer Physik zum Myon-Zerfall"
("New physics contributions to the muon decay"), [ps.gz],
Astrid Bauer (Juli 2002),
supervisor: K. Schilcher

03-D1

"Strahlungskorrekturen zu Zerfallswinkelverteilungen in semileptonischen Bottom-Quarkzerfällen" [ps.gz],
Dagmar Kubistin (September 2003),
supervisor: J. Körner