abstract

These lectures give a description of models with minimal flavour violation (MFV) that can be tested in \(B\) and \(K\) meson decays. This class of models can be formulated to a very good approximation in terms of 11 parameters: 4 parameters of the CKM matrix and 7 values of the universal master functions \(F_r\) that parametrize the short distance contributions. In a given MFV model, \(F_r\) can be calculated in perturbation theory and are generally correlated with each other but in a model independent analysis they must be considered as free parameters. We conjecture that only 5 or even only 4 of these functions receive significant new physics contributions. We summarize the status of the CKM matrix, outline strategies for the determination of the values of \(F_r\) and present a number of relations between physical observables that do not depend on \(F_r\) at all. We emphasize that the formulation of MFV in terms of master functions allows to study transparently correlations between \(B\) and \(K\) decays which is very difficult if Wilson coefficients normalized at low energy scales are used instead. We discuss briefly a specific MFV model: the Standard Model with one universal large extra dimension.

abstract

Hadronic electroweak corrections to the muon anomalous magnetic moment (\(g-2\)) are reviewed. Emphasis is on clarification of discrepancies among various published studies. A theorem on non-renormalization of the transversal part of a correlator of two vector currents and an axial current is reviewed and its consequences in the form of superconvergent sum rules are discussed.

abstract

We present first results of an approach in which all contributions from Zweig-rule-satisfying SU(3)-breaking final-state interactions (FSIs) in \(B\to PP \) decays are taken into account. We include the effects due to Pomeron exchange between the two outgoing pseudoscalar mesons, neglect charmed intermediate states, and express all of the other rescattering effects in terms of only three effective complex parameters. It is pointed out that the experimental bound on the \(B \to K^+K^-\) branching ratio limits the value of only one of these parameters, thus permitting sizable FSI effects in other \(B\) decays. From the fits to the experimental \(B \to PP\) branching ratios we determine the values of the FSI parameters and the weak angle \(\gamma \). A broad range of around \(60^\circ \)–\(100^\circ \) is admitted for the latter, which includes the region expected in the Standard Model.

abstract

Vacuum fluctuations distinguish quantum field theory from non-relativistic quantum mechanics. The phenomena that result from the modification of vacuum fluctuations by external fields or boundary conditions are known as Casimir effects. The study of Casimir effects has been plagued by divergences. In these lectures I describe the framework my collaborators and I have developed for the study of Casimir effects in the context of renormalizable quantum field theories, where divergences can be regulated, analyzed, and, for properly defined observables, removed. I discuss several examples: first a model in which quantum fluctuations stabilize a soliton, next, the physically important case of the Standard Model, where no quantum stabilized soliton has yet been discovered, and finally the “classic” Casimir effect.

abstract

We review how instanton solutions at finite temperature can be seen as boundstates of constituent monopoles, discuss some speculations concerning their physical relevance and the lattice evidence for their presence in a dynamical context.

abstract

In the first three years of running, the four RHIC experiments have collected a rich set of high quality data on nuclear collisions over a wide range in collision energy and system size. The data allow a systematic study of the evolution of the collision system from the initial state to the final freeze-out of hadrons. The measurements show convincingly that in Au+Au collisions at the highest RHIC energies, a dense, interacting medium is formed early on. In this paper, some of the key measurements are described that have revealed the unique and sometimes unexpected properties of this medium.

abstract

The basic ideas which motivated the search for a deconfinement phase transition in high energy nucleus–nucleus collisions are reviewed. The main results obtained within the energy scan programme at the CERN SPS are presented. Several anomalies in energy dependence of hadron production predicted as signals of deconfinement phase transition are observed and they indicate that the onset of deconfinement phase transition is located at about 30 \(A\) GeV. For the first time we seem to have clear evidence for the existence of a deconfined state of matter in nature.

abstract

The Color Glass Condensate is the matter which controls the high energy limit of strongly interacting particles. I qualitatively describe the nature and origin of this matter, and the renormalization group equations which allow for a computation of its properties.

abstract

Statistical hadronization is presented as mechanism for (strange) particle production from a deconfined quark–gluon plasma (QGP) fireball. We first consider hadronic resonance production at RHIC as a test of the model. We present in detail how the hadrochemistry determines particle multiplicities and in case of sudden hadronization allows investigation of QGP properties. A comparative study of strange hadron production at SPS and RHIC is presented. The energy dependence of physical observables shows regularities and a potential discontinuity in the low RHIC range, when comparing these different energy domains. Considering the energy scan program at CERN-SPS we show that the \(K^+/\pi ^+\) discontinuity is a baryon density effect.

abstract

The strong first order nature for more than five colours found in simulations of hot QCD leads to a quasi-particle picture valid down to the critical temperature. We review the evidence for magnetic quasi-particles and suggest simulations that put this picture into evidence.

abstract

At very high temperatures Yang–Mills theories can be described through perturbation theory. At the tree level the time components of the gluon fields decouple and yield a dimensionally reduced theory. The expectation value of the Polyakov loop then assumes values of the \({\rm Z}(N)\) center group. At intermediate temperatures, however, this is not true anymore. The time dependence shows up in loops. In a recent work (D.I. Diakonov, M. Oswald, Phys. Rev. D68, 025012 (2003)) we integrated out fast varying quantum fluctuations around background \(A_i\) and static \(A_4\) fields. We assumed that these fields are slowly varying but that the amplitude of \(A_4\) is arbitrary. As a result we obtained the kinetic energy terms for the Polyakov loop both for the electric and the magnetic sector of SU(2).

abstract

The thermodynamics of the O\((N)\) nonlinear sigma model in \(1+1\) dimensions is studied. We calculate the finite temperature effective potential in leading order in the \(1/N\) expansion and show that at this order the effective potential can be made finite by temperature independent renormalization. We will show that this is not longer possible at next-to-leading order in \(1/N\). In that case one can only renormalize the minimum of the effective potential in a temperature independent way, which gives us finite physical quantities like the pressure.

abstract

Over the next decade hadron colliders will play an important role in the investigation of fundamental questions of particle physics. The high collision energy of the Fermilab Tevatron \(p\bar p\) collider and the CERN Large Hadron Collider (LHC) will allow to probe physics in a new energy domain. In addition, important precision measurements in the area of electroweak physics can be carried out. In particular the experiments at the LHC have a large potential to explore physics beyond the Standard Model and to investigate the nature of electroweak symmetry breaking. In the present article the physics potential of the Tevatron and the LHC is summarized.

abstract

We review the theory and present status of the proton spin problem with emphasis on possible gluonic and sea contributions. We discuss the possibility of a \(J=1\) fixed pole correction to the Ellis–Jaffe sum rule for polarized deep inelastic scattering. Fixed poles in the real part of the forward Compton scattering amplitude have the potential to induce subtraction constant corrections to sum rules for photon–nucleon scattering.

abstract

These lectures trace the origin of string theory as a theory of hadronic interactions (predating QCD itself) to the present ideas on how the QCD string may arise in Superstring theory in a suitably deformed background metric. The role of ’t Hooft’s large \(N_c\) limit, Maldacena’s String/Gauge duality conjecture and lattice spectral data are emphasized to motivate and hopefully guide further efforts to define a fundamental QCD string.

abstract

Last year or so has seen a revival of interest in the dynamics of supersymmetric gauge theories. In this review we give (i) an introduction and a review of the earlier results in the field; (ii) discuss a more recent work of my own and of my collaborators on non-Abelian monopoles, vortices and confinement; and in the last lecture, we discuss (iii) the latest development in the dynamics of \({\cal N}=1\;\) gauge theories.

abstract

Supersymmetric field theories of scalars and fermions in 4D space-time can be cast in the formalism of Kähler geometry. In these lectures I review Kähler geometry and its application to the construction and analysis of supersymmetric models on Kähler coset manifolds. It is shown that anomalies can be eliminated by the introduction of line-bundle representations of the coset symmetry groups. Such anomaly-free models can be gauged consistently and used to construct alternatives to the usual MSSM and supersymmetric GUTs.

abstract

It is recalled that a ten year old calculation of all meson masses may explain the low value of the recently discovered Ds(2317) meson. This calculation was based on a fully relativistic quasiparticle theory, which has been applied to a large number of bound state problems and scattering processes. In this paper we want to show that also for one-dimensional systems the theory can be formulated in a compact way. After discussing the Lippmann–Schwinger equation for two nonrelativistic particles on a line, we show how to extend this momentum–space formulation to a Poincaré invariant theory. We then apply this theory to a simple example and compare the reflection and transmission coefficients, as well as the total diffusion and the bound state spectrum, to the results obtained from the nonrelativistic case. Also the relativistic corrections to the spectrum of two harmonically bound particles are calculated. It is found that especially the higher excited states become less massive.

abstract

We characterize neural networks as approximators of functions and dynamic systems. Neural approximations, leading to nonlinear minimization in highly dimensional spaces, require effective gradient calculation typically realized by gradient backpropagation. We discuss the use of gradient backpropagation for static and for dynamic systems. We also show the essential difference between the common chain rule and backpropagation, which is rarely acknowledged.

abstract

A general setting is presented for the evaluation of several common multivariate analysis techniques including neural networks, support vector machines, and genetic programming. Various theoretical results from pure mathematics and statistical learning theory are presented. Special attention is placed on the optimization criterion for the search for new particles.

abstract

The general framework of the data analyses at LEP is presented, with the emphasis on the application of Artificial Neural Networks in event filtering and parameter estimation.