Members of the Group

Professors:

Heisenberg Fellow and Lecturer:

Post-doctoral assistents and research fellows:

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Research visits of members of the group:

Research funds and support:

Introduction

In a broad sense the research of the group deals with the fundamental interactions of nature and 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 novel extensions of Yang-Mills gauge theories within noncommutative geometry including gravity. More specifically, 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 centers on further development of extended gauge theories within noncommutative geometry, so-called algebraic Yang-Mills-Higgs theories, and 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. Finally, a book project on "Electroweak and Strong Interactions - An Introduction to Theoretical Particle Physics" was completed (F. Scheck, Springer-Verlag, 1996), a revised edition of "Mechanik - Von den Newtonschen Gesetzen zum deterministischen Chaos" was published (F. Scheck, Springer-Verlag, 1996).

Research Projects

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

Extensions of Yang-Mills (gauge) theories to algebraic Yang-Mills-Higgs theories based on Noncommutative Geometry are by now well established. These theories which provide a geometric interpretation of spontaneous symmetry breaking and which incorporate chiral fermions as dynamic building blocks, aim at a novel unified description of electroweak, strong and gravitational interactions. Our group was the first in Germany who took up this field of research about a decade ago and had an active share in its development. Over the period covered by this report we have continued work on the model developed in Mainz and Marseille and its applications to particle physics [MZ-TH/97-01, MZ-TH/97-08, MZ-TH/97-29]. In parallel we have studied specific questions in the framework of Connes' spectral triple approach such as the attempt to incorporate spacetime-supersymmetry in this approach [MZ-TH/96-07], the intriguing topic of possible mass relations in noncommutative geometry [MZ-TH/97-08], and the possibility of incorporating leptoquarks [MZ-TH/97-31].

2. Mass Matrices and Mixing of Weak Interaction States (F. Scheck et al.)

The Cabibbo-Kobayashi-Maskawa mixing matrix for quarks and, most likely, an analogous mixing matrix for neutrinos governing neutrino oscillations, are manifestations of the mismatch between the mass eigenstates and the weak interaction states (i.e. those which are produced at weak interaction vertices with charged currents). 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 (differing by one unit) each. The latter, however, are highly ambiguous and any attempt to reconstruct them from the observed mixing has to cope with high-dimensional manifolds of choices.

With the aim of organizing the extraction of mass matrices from the observed mixing in an optimal way, 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 [MZ-TH/97-29]. 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 differencies and of mixing in a most transparent manner. Already our first attempts are in fair agreement with CKM-mixing of quarks, and with neutrino oscillations regarding the MSW effect for solar neutrinos as well as atmospheric neutrinos [MZ-TH/97-29, MZ-TH/97-36]. Further applications of this method of analysis are in progress.

3. Connes' Non-Commutative Geometry, Hopf Algebras and the Fundamental Interactions (F. Scheck et al.)

Connes' noncommutative 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 [MZ-TH/96-08, MZ-TH/96-22, MZ-TH/96-23, MZ-TH/97-14], the classification of finite Spectral Triples and their relation to Hopf algebras [MZ-TH/96-40, MZ-TH/97-22] and applications thereof [MZ-TH/97-31]. Although of a more formal nature these investigations are important in our quest to understand the detailed structure of spacetime as indicated by the physics of the standard model and, eventually, to get hints of how to reconcile gravity and quantum theory.

4. Knots, Numbers, Feynman Diagrams (D. Kreimer et al.)

Knot theory together with gauge symmetry explain the rationality of the quenched beta-function [MZ-TH/95-22]. - Non-perturbative methods verify the identification of double sums with 2-braid knots [MZ-TH/95-28]. - A connection between Quantum Field Theory, knot theory and number theory was discovered [MZ-TH/96-18]. - Knot Theory and calculation of Feynman diagrams establish new conjectures in number theory [MZ-TH/96-25]. - The connection between knot theory and Feynman diagrams was established for subdivergent graphs [MZ-TH/96-31]. - Feynman diagrams can form a weight system under appropriate conditions [MZ-TH/96-36]. - The structure of the weight system verified to the 5-loop level [MZ-TH/96-37]. - Renormalization was recovered as a Hopf algebra. The antipode corresponds to the forest formula [MZ-TH/97-25].

5. Anomalies in Perturbative Quantum Field Theory (D. Kreimer et al.)

The chiral anomaly in spacetimes with torsion reduces to the expected contributions including Pontrjagin classes. The Nieh-Yan term is shown to be absent [MZ-TH/97-18].

6. Geometrical Methods in Classical and Elementary Particle Physics (N. Papadopoulos 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 serious implications in many fundamental problems in elementary particle physics. In this project, we investigate on quantization in various ways: within the framework of noncommutative geometry, deformation quantization, BRS formalism, quantum groups and Hopf algebras (see diploma theses by S. Nitzsche, A. Köhler, J. Höhle, M. Mertens).

7. Noncommutative Geometry Approach to Elementary Particle Physics (N. Papadopoulos et al.)

The physical assumptions on which the noncommutative approach to elementary particle physics rely are investigated. On this basis a class of new models is presented [MZ-TH/97-24].

8. Theoretical Aspects of Charged-Composite Particle Scattering (E. O. Alt et al., supported by DFG, Project 436 USB-113-1-0 and by DAAD)

Modern analyses of few-particle reactions are successfully based on momentum space integral equations of the Faddeev type, provided the interparticle interactions are of short range. For, the presence of long-range Coulomb interactions poses problems for the theory which are still to a good part unresolved. This is especially so when the three charged particles can escape to infinity (breakup or ionisation).

For the investigation of the properties of the effective interactions between the colliding clusters, knowledge of the asymptotic behaviour of the three-body Columb Green function is required for regions of configuration space where two of the particles are closer to each other than the third one from their center of mass. This information has recently been provided in [MZ-TH/92-45]. With its help the first nonperturbative derivation of the long-range behaviour of the optical potential had been performed [MZ-TH/94-25]. As a sequel, a new rather long range component has been identified recently [M1, M2].

Another application of the asymptotic behaviour of the three-body Columb Green function concerns the singularity structure of the kernel of the integral equations of charged-composite particle scattering. Already in the two-charged elementary particle case, the infinite range of the Coulomb potential is identified as the source of a nonintegrable singularity of the kernel which results in the non-applicability of the integral equations method, and of other peculiarities of Coulombian quantities. Within the framework of the effective two-body formulation of three-body equations we have now succeeded to prove that for two-cluster reactions of three charged particles, the only nonintegrable singularities occur in the diagonal kernels and, moreover, that the latter are of the two-body type and hence can be dealt with in the standard manner, leading at the end to compact kernel equations. According to our present knowledge this result holds true for purely repulsive Coulomb interactions only. Preliminary results have been communicated in [MZ-TH/97-12,A]. A full version is in preparation.

9. Application of Three-Body Methods to Atomic Collisions (E. O. Alt et al., supported by DFG, Project 436 USB-113-1-0 and by DAAD)

Many atomic processes are of three-body type as, e.g. electron transfer or charge-exchange. The above mentioned fundamental problems of integral equations are expected to be less desastrous for higher energies since there the first few terms of a multiple scattering expansion of the scattering amplitude are expected to be adequate. Nevertheless, there have been only few, and not particularly successful, applications of few-body methods to atomic reactions. The major practical reason is the occurrence of the two-body Coulomb T-matrix in the multiple scattering terms; the latter is a rather nasty since highly singular quantity, with regard to the on-shell limit, to existence of partial-wave projections and convergence of partial-wave summations, and for attractive Coulomb potentials because of the infinity of bound states (some of these aspects are described in detail in [MZ-TH/95-05]).

We have succeeded for the first time to exactly calculate numerically the leading first-order rescattering contributions ("triangle amplitudes"), for repulsive as well as for attractive Coulomb potentials. For the latter case a new representation of the Coulomb T-matrix had to be developed which has the bound state poles separated in an explicit, numerically convenient way. But the numerical calculations are found to be very time consuming. Hence, by applying refined analytical methods, approximate analytical expressions for these triangle amplitudes have been developed which are rather easy to use. Their quality and their region of applicability has been thoroughly tested. Besides, a variety of bounds and approximate relations has been derived for the triangle amplitudes which should be useful for qualitative estimates. The results are published in [MZ-TH/95-29, MZ-TH/96-01, MZ-TH/96-12, MZ-TH/96-13, MZ-TH/97-13, MZ-TH/97-06, MZ-TH/97-07, MZ-TH/97-10, AKM9], a brief summary is given in [MZ-TH/97-33]. Applications to a unified description of proton-hydrogen atom elastic and exchange scattering are in preparation.

10. Coulomb Effects in Nucleon-Deuteron Scattering (E. O. Alt et al., DFG, Project 436 USB-113-1-0)

The investigation of nucleon-deuteron (Nd) scattering is of crucial importance since it is the simplest reaction which is sensivtive to off-shell effects of the fundamental NN interaction and to the equally fundamental three-nucleon forces. It therefore belongs to the experimentally most extensively studied nuclear interactions. On the theoretical side, a long development of appropriate numerical techniques over the past two decades has resulted in rather complete understanding of various observables, based on the most sophisticated two-and three-nucleon potential models, but only for the neutron-deuteron (nd) reaction where the experimental data are much less abundant and much less accurate. The wealth of the very precise proton deuteron (pd) data has up to now been analysed with comparable sophistication below the breakup threshold only; for higher energies, and in particular for the deuteron breakup reaction itself, only simple NN force models have been used as yet, because of the enormous complexity of the equations to be solved.

By applying the 'screening and renormalisation method' [MZ-TH/95-05], which is up to now the only theoretically satisfactory approach for including the long-range Coulomb forces for energies above the breakup threshold, we have succeeded to perform for the first time calculations of pd elastic scattering observables at positive energies with the realistic "Paris" NN potential (in its so-called PEST1-6 form which is known to provide an excellent approximation to the original potential). The NN interaction is taken into account in the states ₃S¹ - ₁S⁰ and in all p-waves. While differential cross sections are perfectly described there remain discrepancies in polarisation observables, implying that some aspects of the nuclear force are not yet fully accounted for in our calculation although the general trends suggested by the data, in particular concerning the relation between neutron and proton data, are well reproduced. Possibilities for further improvement would consist in taking into account still higher NN partial wave contributions, use of more modern potentials and eventually inclusion of three-body forces. However, one observation is indisputable: any agreement of nd-calculations with pd-data, in particular for iT₁₁ and also to a somewhat lesser extent for A_y, is purely fortuitous and does not arise from smallness of Coulomb effects in that observable. First results have been communicated in [MZ-TH/97-26]; further publications are in progress.

A final comment concerns the fact that in our calculations the Coulomb interaction is taken into account in the so-called Coulomb-Born approximation. However, as we have shown [MZ-TH/97-11] the latter provides an excellent approximation to the exact Coulomb contribution for nuclear processes with lowly-charged particles (although it dramatically fails for typical atomic reactions).

11. Post-Acceleration Effects in the Coulomb Breakup of Light Nuclei (E. O. Alt et al., supported by the DAAD)

Knowlege 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 neutrino fluxes, etc. Direct measurements are greatly impeded by the required low energy of the fusing nuclei. Hence, as an alternative the inverse process, namely the Coulomb breakup in the field of a heavy, fully stripped nucleus, has been proposed and first experiments have been performed. However, in order to be able to extract the S-factor from such reactions one must assume that the nucleus only serves a source of photons to induce the breakup, but has no influence on the ejectiles afterwards. However, from the behaviour of the three-charged particle wave function in the appropriate asymptotic regions [AM93, ML] it is known that long-range three-body correlations occur which, depending on projectile and ejectile energies, can considerably modify such a simple picture ("post-acceleration effects") as we have already shown previously [IMMA].

We have now applied these ideas to the study of the dissociation of ₈B into ₈Be + p in the Coulomb field of a fully stripped ₂₀₈Pb ion for which recently experimental data have been published (T. Motobayashi et al., Phys. Rev. Lett. 73 (1994) 2680) and several new experiments are under way (₈B decay is the major source of high energy neutrinos). Our calculations are based on the DWBA, using a final state three-body wave function which has the (extended) correct asymptotic behaviour [MZ-TH/92-45, ML]. We show that three-body effects do, indeed, give sizeable contributions to the double differential cross-section for ₂₀₈Pb (₈B, ₇Be p) ₂₀₈Pb, when the fragments ₇Be and p have small relative energies. For instance, at 300 keV relative energy the cross section is enhanced in the maximum around 2 degrees scattering angle by 10 - 20% over the standard result (without three-body correlations). For larger angles and for higher relative energies the three-body contributions quickly die out. But in order to extract a reliable S-Factor for ₈B production, experimental cross sections of ₈B breakup are needed at as low as possible energies. Hence, our calculations indicate that below 600 keV, three-body Coulomb FSI-effects must not be neglected in the analysis of experimental data [AIM].

References (not Mainz preprints)
M1: "Three-body effect: Nonrelativistic 1/p⁵ polarisation term in the effective potential between charged particles", A. M. Mukhamedzhanov, Phys. Rev. A56 (1997) 473.
M2: "A new three-body effect: Nonrelativistic 1/p⁵ polarisation term in the effective potential between charged particle and neutral system", A. M. Mukhamedzhanov, Proc. of "XV. Int. Conf. on Few-Body Problems in Physics", Groningen 1997, p. 146ff.
AKM9: "Total and differential cross sections for electron transfer and capture in proton-hydrogen scattering", E. O. Alt, A. S. Kadirov, A. M. Mukhamedzhanov (in preparation).
ML: A. M. Mukhamedzhanov, M. Lieber, Phys. Rev. A54 (1997) 3078.
IMMA: "Coulomb breakup of fast light ions with taking into account three-body Coulomb effects", B. F. Irgasiev, A. T. Muminov, A. M. Mukhamedzhanov, Tr. J. of Phys. 20 (1996) 111.
AIM: in preparation.

12. Determination of the Strange Quark Mass (K. Schilcher et al.)

A precise determination of the strange quark mass is of crucial importance for a better understanding of low energy phenomenology of the standard model, e.g. for a precise prediction of the CP-violating parameter '. Using new four loop results in the systematic operator product expansion for the correlator of two scalar currents, chiral perturbation theory and experimental K phase shifts in a sum rule analysis we find m_s (1GeV) = 205 R± 19 MeV [MZ-TH/96-19, MZ-TH/96-27]. This result is in agreement with direct determinations from -decay, but in strong disagreement with the very small value of recent lattice QCD calculations.

13. Two-Loop Calculations in Chiral Perturbation Theory (K. Schilcher et al.)

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 desireable. The question of convergence of the chiral expansion is addressed [MZ-TH/97-02]. The electromagnetic form factor of the neutral kaon ist 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 [see: "Electromagnetic form factor of the neutral kaon in O(p⁶) chiral perturbation theory", P. Post, K. Schilcher, to be submitted for publication]. Finally all electromagnetic and semi-leptonic form factors of pions and kaons were calculated in the same order. The predictive power turns out to be limited, due to the large number of arbitrary renormalization constants (see the doctoral thesis by P. Post).

14. Rare Kaon Decays (K. Schilcher et al.)

Rare decays of kaons constitute a sensitive laboratory to look for possible extensions of the Standard Model. The lepton-flavour violating decay K_L e µ was studied in detail within the context of SU(2)_R×SU(2)_L×U(1)_(B-L) models, which include heavy Majorana neutrinos. A fully gauge invariant one-loop analysis was carried out. We find that the branching ratio B(K_L e µ) can be considerably enhanced and can reach values close to, or even larger than the present experimental limit of 3.3 × 10^-11. Constraints on the parameter space of typical left-right models are derived in a global analysis of all relevant low-energy data [MZ-TH/97-28].

15. Technical Aspects of Massive Two-Loop Feynman Diagram Calculations (K. Schilcher et al.)

In the framework of the wider project of calculating massive multi-loop Feynman diagrams, the problem of infrared and collinear divergences is investigated. Results and calculational techniques of two groups are compared. Two-loop vertex Feynman diagrams with infrared and collinear divergences are studied, on the one hand, by a small-momentum expansion augmented by Padé techniques and, on the other hand, by a numerical method using light coordinates in the parallel space. The results of the two methods agree [MZ-TH/97-20].

16. Electrical Impedance Tomography (EIT) (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. One of the problems of the EIT is that the skin-electrode resistance does not follow Ohm's law. It could be shown, that the problem can be circumvented, if no information on the conductivity close to the skin is required [MZ-TH/95-09]. 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. The effect of the third dimension was therefore studied in detail, both in model calculations and in comparison with real data (see doctoral thesis by I. Savelsberg).

17. Test of QCD Perturbation Theory (K. Schilcher et al.)

In perturbative quantum chromodynamics, moments of the total e⁺e^--annihilation cross section can be related to the decay rate. In this way the decay rate replaces the conventional strong coupling constant _s as the expansion parameter of QCD. If the integration in the e⁺e^- moments extends to m ², cancellations of unknown terms occur, and one obtains predictions for observables with one more term in the QCD perturbation theory than was ever calculated before [MZ-TH/97-09]. The analysis was extended in [MZ-TH/97-16] where a partial all order resummation of the perturbation series was performed by solving the renormalization group equation for Adler's function in the complex plane. The all order analysis considerably improves the theoretical reliability of the comparison of -decay and e⁺e^--annihilation data. In [MZ-TH/97-03] we extract the value of _s from semileptonic -decay data again performing a partial all order resummation of the perturbation series in _s. Our analysis includes the recently calculated four-loop value of the -function in QCD. As a by-product we determine the exact value of the convergence radius of the perturbation series in -decay by analyzing the singularity structure of the complex coupling plane.

18. Heavy Quark Effective Theory (J. G. Körner et al.)

The Heavy Quark Effective Theory (HQET) consists in an expansion of the QCD Lagrangian in terms of inverse powers of the heavy quark mass not unlike the case of the Fouldy-Wouthuysen transformation in QED. In this way the heavy mass scale is explicitly factored out and one remains with effective heavy quark fields which no longer depend on the heavy quark mass scale. In the simplest tree-level version the requisite Foldy-Wouthuysen type transformation has been carried out to a very high order in Mainz. The mass independent coefficient functions become renormalized through quantum loop effects which may also induce new operators involving heavy quark fields not present at tree level. In [MZ-TH/96-17] we determined the coefficients of a new class of HQET operators which arise at the one-loop level and involve the product of heavy and light (spectator) quark fields and thus affect the calculation of mass splittings of heavy mesons within HQET. From Lorentz invariance the coefficients in the heavy mass expansion of the QCD Lagrangian become related to one another at every loop order. These so-called reparametrization invariance relations are worked out in [MZ-TH/96-17, MZ-TH/96-18] up to O(1/m²). The next issue in HQET concerns the evaluation of matrix elements between heavy particles. Although the heavy-side dynamics is calculable in the heavy mass expansion one remains with the light-side dynamics which must be analyzed by traditional means. In [MZ-TH/95-20, MZ-TH/95-31] well-known techniques from the light particle sector (Adler-Weisberger relation, Compton scattering sum rules) were used to derive a class of new sum rules and conservation laws that help to constrain the light-side dynamics in heavy meson to heavy meson transitions. An important class of sum rules are the zero recoil sum rules at zero velocity transfer for current-induced transitions between heavy particles. The O(_s) corrections to these sum rules were worked out in [MZ-TH/94-24] which lead to an improved determination of the zero-recoil value of the Isgur-Wise function.

19. Applications of HQET: Current, Pion and Photon Transitions Between Heavy Baryons (J. G. Körner et al.)

In a number of papers we considered various phenomenological applications of HQET to heavy baryons involving current, pion and photon transitions. These phenomenological applications involved the modelling of the light-side dynamics to various degrees of sophistication. In [MZ-TH/95-21, MZ-TH/95-27, MZ-TH/95-33] we looked at polarization phenomena in the inclusive semileptonic decays of a heavy _b-baryon. The inclusive semileptonic decays can be described by HQET in terms of a few universal nonperturbative matrix elements of the _b-baryon. In [MZ-TH/95-21, MZ-TH/95-33] we took a detailed look at various spin observables in these decays including spin correlation observables and worked out how they depend on the basic nonperturbative matrix elements. Ref. [MZ-TH/95-27] is devoted to the optimization of the measurement of the _b-polarization in its inclusive semileptonic decay through a measurement of spin-momentum correlations between the spin of the _b and the momentum of the lepton in the decay. Current, pion and photon transitions between heavy baryons involve the unknown transitions between the light diquark states in the heavy baryon. In the simplest approach the light-side diquark transitions can be modelled using the constituent quark model approach which is known to work very well phenomenologically in the light quark sector. In [MZ-TH/95-15] we worked out the constituent quark model relations between the various reduced HQET form factors in current-induced heavy baryon transitions. Similar relations were written down for pion transitions in [MZ-TH/96-10] and for photon transitions in [MZ-TH/96-38]. In [MZ-TH/96-32] we employed the field theoretic "Relativistic Three-Quark Model" developed earlier to calculate the transition form factors in the exclusive semileptonic decay _{b c} l and to compare the results to the corresponding HQET calculation. The same model was used to calculate the exclusive nonleptonic decays of the _c including the nonfactorizing contributions [MZ-TH/97-15, MZ-TH/97-21]. Our results on the applications of HQET to heavy baryon decays were reported at a number of workshops and meetings [MZ-TH/96-04, MZ-TH/96-09, MZ-TH/96-24].

20. Massive Two-Loop Integrals (J. G. Körner et al.)

In the last few years a large part of the theoretical particle physics group in Mainz has been involved in the computation of massive one- and two-loop Feynman integrals. This activity was part of a continuing group seminar series on the evaluation of Feynman diagrams. One of the goals of this activity was to develop a user-friendly program that automatically calculates massive one- and two-loop Feynman integrals (two, three and four point functions) including their renormalization. A first version of the program XLOOPS has been realized and is described in [MZ-TH/96-30, MZ-TH/96-39, MZ-TH/97-23, MZ-TH/97-32, MZ-TH/97-35]. A detailed account of what XLOOPS can do in the present version and how to use XLOOPS is given in the manual [MZ-TH/96-20]. Generally speaking 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. We developed an efficient parallelization of our adaptive Monte-Carlo integration code to speed up the numerical calculations [MZ-TH/97-30]. First attacks on the handling of two-loop infrared problem in the presence of massless particles were successfully completed [MZ-TH/97-20, MZ-TH/97-37]. A calculation of one-loop corrections to Higgs decay in the Higgs doublet model [MZ-TH/96-16] lead to the incorporation of the two Higgs doublet model Feynman rules into XLOOPS. The partial branching fractions of Higgs decay into various channels were calculated at the two-loop level: Higgs into two photons [MZ-TH/95-18], Higgs into two massive fermions [MZ-TH/95-30] and Higgs into two gauge bosons [MZ-TH/96-15], where the calculations [MZ-TH/95-18, MZ-TH/96-15] were done in the effective high energy approximation using the Equivalence Theorem for massive gauge bosons. The calculation [MZ-TH/95-18] was done using the disperse-absorptive approach to two-loop calculations where one first calculates the absorptive parts of the contributing Feynman diagrams and then uses dispersion relations to obtain the real part. The disperse-absorptive technique was also used in [MZ-TH/96-14] to obtain one-dimensional integral representations of the two-loop sunset diagram. For the calculation [MZ-TH/96-15] a new representation was found for the two-loop crossed ladder configuration [MZ-TH/96-30] which is ideally suited for implementation in XLOOPS. One of the first applications of XLOOPS resulted in the determination of the two-loop flavour changing wave-function renormalization of e.g. the s d transition [MZ-TH/96-19]. A first estimate of two-loop corrections to the decay were given in [MZ-TH/96-33]. New interesting multi-loop techniques concerning tensor integration methods and calculations in higher dimensions were explored in [MZ-TH/95-14, MZ-TH/95-26] which might eventually find their applications in later versions of XLOOPS.

21. Radiative Corrections to Heavy Quark Production in e⁺e^--Annihilation (J. G. Körner et al.)

After the discovery of the heavy top quark at the Tevatron in 1995 there has been a great deal of interest in the use of the planned high energy linear e⁺e^--collider as a copious source of top quark pairs. When the linear collider comes into operation it is necessary to have available detailed radiative QCD corrections to the production and decay of top quark pairs. There are a number of unpolarized and single spin polarized structure functions that describe the leptonic e⁺e^--production process of top quark pairs. Whereas the O(_s) corrections to the unpolarized structure functions had been calculated before the O(_s) corrections to the polarized structure functions were first calculated in a series of papers in Mainz [MZ-TH/95-09, MZ-TH/95-17, MZ-TH/95-19]. This includes the cases of transverse polarization [MZ-TH/95-17] and longitudinal polarization [MZ-TH/95-17, MZ-TH/95-19]. We have started to embark on a program to calculate also the O(_s) corrections to double spin asymmetries starting with longitudinal spin correlations in [MZ-TH/97-27]. Other O(_s) effects in this process were studied in [MZ-TH/96-34, MZ-TH/97-17, MZ-TH/97-39]. [MZ-TH/96-34, MZ-TH/97-17] contains an analysis of gluon polarization effects while we studied the rigidity of back-to-back top quark pairs against gluon radiation in MZ-TH/97-39]. In an O(_s²) calculation it was shown how the tagging of b-quark jets in e⁺e^--annihilation may be exploited to considerably improve on the determination of the three-gluon coupling structure of QCD [MZ-TH/95-10, MZ-TH/96-29]. Radiative interference effects both in the production and in the decay of top quark pairs were studied in [MZ-TH/95-01, MZ-TH/96-05] with particular emphasis on the question of how the top mass determination is affected by radiation effects. The same issue concerning W-pair production and the W mass measurement in this process was adressed in [MZ-TH/95-03].

22. QCD Sum Rules for Heavy Baryons (J.G. Körner et al.)

The nonperturbative vacuum matrix elements of the correlators of the heavy baryon currents were analyzed in the framework of QCD sum rules using Borel transform techniques. The analysis of previous authors was improved on in that the next-to-leading QCD radiative corrections to the sum rules were fully included. This necessitated the computation of the two-loop O(_s²) corrections to the anomalous dimension of the heavy baryon currents [MZ-TH/96-06] and the O(_s) corrections to the current-current correlators [MZ-TH/96-21, MZ-TH/97-19]. Because there exist two interpolating baryon currents for each of the ground state heavy baryon states the QCD sum rules have a two-by-two structure corresponding to diagonal and nondiagonal current transitions. The diagonal [MZ-TH/96-21] and nondiagonal sum rules [MZ-TH/97-19] were analyzed using Borel techniques resulting in a new determination of the current residues, the masses and the binding energies of the ground state heavy baryon states. The effect of the next-to-leading QCD corrections on the sum rule analysis were found to be substantial. The results of the next-to-leading analysis were reported at a number of workshops and conferences [MZ-TH/96-26, MZ-TH/97-05, MZ-TH/97-34].

23. Proton-Proton Annihilation (J.G. Körner et al.)

The annihilation of protons and antiprotons at rest into two ground state mesons was analysed within four different extended SU(3) schemes corresponding to s-, t- and u-channel coupling schemes and a quark flavour flow coupling scheme. The group theoretical relations between the various coupling schemes were worked out. Based on recent data on proton-antiproton and neutron-antineutron annihilation the coupling parameters occurring in the various coupling schemes were extracted from the data and were scrutinized in terms of various model assumptions concerning the annihilation dynamics [MZ-TH/95-23].

24. W-Production at -Colliders (J.G. Körner et al.)

In the collision of unstable particles as in the collision of the muon pairs the foreseen-collider one can encounter a new type of singularity in the physical scattering region due to the fact that the initial particle is unstable and its real decay can take place. A prototype of such a singular process is the annihilation process W. In a series of papers it was shown for the first time that the singular behaviour of such annihilation processes becomes regularized when the transverse beam spread of the colliding muon beams is taken into account [MZ-TH/96-02, MZ-TH/96-03, MZ-TH/96-11]. The cross section is found to be directly proportional to the geometrical beam size of the initial beams.

Scientific Papers, Publications and Conference Contributions

PhD Theses

"Precision tests of the standard model at future linear colliders",
K. Melnikov (1996),
supervisor: J. G. Körner,
supported by Graduiertenkolleg "Teilchenphysik".

"Virtuelle Strahlungskorrekturen im Standardmodell der Elementarteilchenphysik", [97-T1],
J. Franzkowski (1997),
supervisor: J. G. Körner,
supported by Graduiertenkolleg "Teilchenphysik".

"QCD Strahlungskorrekturen in der Physik schwerer Quarks und Baryonen" (Radiative QCD corrections in the physics of heavy quarks and baryons), [96-T1],
S. Groote (1997),
supervisor: J. G. Körner,
supported by DFG (Deutsche Forschungsgemeinschaft).

"Nichkommutative Geometrie und Gravitation",
M. Walze (Mai 1996),
supervisor: F. Scheck.

"Von Fredholmmodulen zu Spektralen Tripeln in nichtkommutativer Geometrie",
J.-M. Warzecha, (November 1997),
supervisor: F. Scheck.

"Automatische Berechnung von Strahlungskorrekturen in perturbativen Quantenfeldtheorien" (Authomatic calculation of radiative corrections in perturbative quantum field theories), [97-T3],
Lars Brücher (November 1997),
supervisor: K. Schilcher.

"Elektromagnetische und schwache Vektorformfaktoren des pdeudoskalaren Mesonoktetts zur Ordnung p⁶ der chiralen Störungstheorie", [97-T2],
P.Post (1997),
supervisor: K. Schilcher.

"Elektrische Impedanztomographie mit realistischen Daten", [98-T1],
I. Savelsberg (1998),
supervisor: K. Schilcher.

Diploma Theses

"Ein quantendeformierter Cartan-Kalkül",
Sven Nitzsche,
supervisor: N. Papadopoulos.

"Aspekte des BRST-Formalismus",
André Köhler,
supervisor: N. Papadopoulos.

"Anomalien und Determinantenbündel im Rahmen der Atiyah-Singer Indextheoreme",
Jörg Höhle,
supervisor: N. Papadopoulos.

"Hopfalgebren-Struktur und Quantisierung",
Mathias Mertens,
supervisor: N. Papadopoulos.

State Examination Theses

"Ein relativistisches Spin-0-Teilchen im Kastenpotential",
Simone Jüngling, 1996,
supervisor: E. Trübenbacher.

"Streuung relativitischer Spin-0-Teilchen am eindimensionalen Kastenpotential",
Dirk Müller, 1996,
supervisor: E. Trübenbacher.

"Untersuchungen zum relativistischen Tunneleffekt für Spin-0-Teilchen am eindimensionalen Kastenpotential",
Andreas Frößl, 1997,
supervisor: E. Trübenbacher.