We discuss all possible schemes with four massive neutrinos inspired by the existing experimental indications in favour of neutrino mixing, namely the atmospheric, solar and LSND neutrino experiments. We argue that the scheme with a neutrino mass hierarchy is not compatible with the experimental results, likewise all other schemes with the masses of three neutrinos close together and the fourth mass separated by a gap needed to incorporate the LSND neutrino oscillation result. Only two schemes with two pairs of neutrinos with nearly degenerate masses separated by this gap of the order of 1 eV are in agreement with the results of all experiments, including those where no indications for neutrino oscillations have been found. We also point out the possible effect of big-bang nucleosynthesis on the 4-neutrino mixing matrix and its consequences for neutrino oscillations. Finally, we study predictions for neutrino oscillation experiments and \(^3\)H and \((\beta \beta )_{0\nu }\) decays, following from the two favoured neutrino mass spectra and mixing schemes. These predictions can be conceived as checks of the input used for arriving at the two favoured schemes.

Using the result of the three flavor analysis of the old Kamiokande data, the recent Superkamiokande data of atmospheric neutrinos and the CHOOZ reactor data, it is shown that the third mixing angle \(\theta _{13}\) is small. It is proposed to determine the small value of \(\theta _{13}\) and the CP violating phase \(\delta \) in very long baseline experiments by measuring the appearance probability \(P(\nu _\mu \rightarrow \nu _e)\) and the T violating effect \(P(\nu _e\rightarrow \nu _\mu )-P(\nu _\mu \rightarrow \nu _e)\) which are enhanced by the matter effect of the Earth.

Recent atmospheric neutrino data at Super-Kamiokande suggest the large flavor mixing of neutrinos. Models for the lepton mass matrix, which give the near-maximal flavor mixing, are discussed in the three family model. Especially, details of the models with the S\(_3\) or O(3) flavor symmetry are studied.

In spite of the general belief that neutrinos are Majorana particles, their character should be revealed experimentally. We begin by discussing why it is so difficult in terrestrial experiments. If neutrinos are Majorana particles, the first signal should come from neutrinoless double \(\beta \) decay. Still the search for such a decay of various nuclei is negative. We outline how the present knowledge of neutrino masses and mixing matrix elements combined with the bound from \(\left ( \beta \beta \right ) _{0\nu }\) decay could help to determine their nature.

We study the simplest Standard Model extension with only one extra right-handed neutrino. In this case there are two massless \(m_{1,2}\) and two massive \(m_{3,4}\) neutrinos, and in principle both solar and atmospheric anomalies can be described in two different scenarios, \(m_3 \ll m_4\) (scheme I) and \(m_3 \simeq m_4\) (scheme II). However, neither bi-maximal mixing nor the dark matter problem are explained in this minimal extension. Only scheme II can accommodate simultaneously maximal mixing for atmospheric neutrinos and the small mixing angle MSW solution for the solar anomaly. This scenario can be tested in the BOREXINO experiment.

Gravity compresses the matter in the cores of neutron stars to densities which are significantly higher than the density of ordinary atomic nuclei, thus providing a high-pressure environment in which numerous particle processes — from the generation of new baryonic particles to quark deconfinement to the formation of Boson condensates and H-matter — may compete with each other. There are theoretical suggestions of even more ‘exotic’ processes inside pulsars, such as the formation of absolutely stable strange quark matter, a configuration of matter even more stable than the most stable atomic nucleus, iron. In the latter event, neutron stars would be largely composed of pure quark matter, eventually enveloped in nuclear crust matter. No matter which physical processes are actually realized inside neutron stars, each one leads to fingerprints, some more pronounced than others though, in the observable stellar quantities. This feature combined with the tremendous recent progress in observational radio and X-ray astronomy, renders neutron stars to nearly ideal probes for a wide range of dense matter studies, complementing the quest of the behavior of superdense matter in terrestrial collider experiments.

Several aspects of the structure of neutron stars are considered from theoretical and observational perspectives. Theoretical limits on the mass and radius are considered, and these are compared with new observations of isolated neutron stars and quasi-periodic oscillators (QPOs). A radius determination provides information concerning the nuclear symmetry energy and its density dependence, but does not much constrain the stiffness of the EOS, contrary to popular belief. Three analytic structure solutions are discussed which shed light on other structural aspects of neutron stars, including their moments of intertia and binding energies. Pulsar glitches may constrain the distribution of the moment of inertia inside a star and supernova neutrinos, marking the birth of a neutron star, may constrain the neutron star’s binding energy.

Laser interferometric experiments planned for 2002 will open up a new window onto the Universe. The first part of the paper gives a brief intuitive introduction to gravity waves, detection techniques and enumeration of main astrophysical sources and frequency bands to which they contribute. Then two more specific issues are discussed concerning cosmological perspectives of gravity waves detection. First one is the problem of gravitational lensing of the signal from inspiralling NS–NS binaries. The magnitude of the so called magnification bias is estimated and found non-negligible for some quite realistic lens models, but strongly model-dependent. The second problem is connected with estimates of galactic and extragalactic parts of the stochastic background. The main conclusion from these two examples is that in so far as the cosmological payoff of gravitational wave detection would be high, we should substantially deepen our understanding of basic astrophysical properties of galaxies and their clusters (in terms of mass distribution) in order to draw clear cosmological conclusions.

The latest preliminary results of the searches for Higgs bosons and Supersymmetric particles at LEP are reviewed. The results include the data-taking in 1999 up to center-of-mass energies of 196 GeV. The combination of the results from the four LEP experiments leads to a significant increase of the detection sensitivity. No indication of a signal has been observed. In the Standard Model (SM) a lower limit of 102.6 GeV on the mass of the Higgs boson is set at 95% CL. In extended models, stringent limits are also set on the \(HZZ\) coupling. Interpretations in the Minimal extension of the Supersymmetric Standard Model (MSSM) are given and the importance of general MSSM parameter scans is emphasized. In general scans, the limit on the mass of the lightest scalar Higgs boson is about 7 GeV lower in comparison with benchmark results. The data also constrains charged Higgs bosons of a general two-doublet model and Supersymmetric partners of the SM particles.

After reviewing the theoretical formalism of \(\varepsilon '/\varepsilon \) and the predictions of the Standard Model, I describe the detectors of the NA48 and KTeV collaborations. The analysis methods of the two groups are compared. The two new measurements of the parameter Re \((\varepsilon '/\varepsilon )\) are presented.

We review the generalized vector dominance (GVD) approach to DIS at small values of the scaling variable, \(x\). In particular, we concentrate on a recent formulation of GVD that explicitly incorporates the configuration of the \(\gamma ^{\ast } \to q{\bar q}\) transition and a QCD–inspired ansatz for the \((q{\bar q})p\) scattering amplitude. The destructive interference, originally introduced in off-diagonal GVD is traced back to the generic structure of two-gluon exchange. Asymptotically, the transverse photoabsorption cross section behaves as \((\ln Q^2)/Q^2\), implying a logarithmic violation of scaling for \(F_2\), while the longitudinal-to-transverse ratio decreases as \(1/\ln Q^2\). We also briefly comment on vector–meson production.

DA\(\Phi \)NE will offer an opportunity to check Chiral Perturbation Theory predictions at higher order. In this talk I have selected a few topics for which it is expected that the lowest order calculation will not be sufficient in order to compare with the experimental results. In particular I will discuss pion pair production in two photon collisions, \(K_{l_3}\) and \(K_{l_4}\) decays.

The top flavour-changing neutral couplings can be large in extended models with vector-like quarks. In the next decade(s) the CERN Large Hadron Collider will allow to measure (bound) them with a precision of few per cent.

Recent progress in calculations of the total cross section for top quark pair production near threshold is reviewed. Different top quark mass definitions adequate for threshold studies are discussed. A relation between the potential subtracted mass and the 1S mass is studied. The potential subtracted 1S mass is defined which incorporates attractive features of both schemes.

We review the results on representing the differential cross section for \(W\)-pair production, including \(W\) decay and hard-photon bremsstrahlung, in terms of a Born-form approximation of fairly simple analytic form.

An efficient method for calculating polarized matrix elements of the four fermion reactions \(e^+ e^- \rightarrow 4f\) and corresponding hard bremsstrahlung reactions with non-zero fermion masses is discussed. The numerical results for the total cross sections and some differential cross sections of \(e^+e^-\to u\bar d\mu ^-\bar \nu _\mu \) and \(e^+e^-\to u\bar d\mu ^-\bar \nu _\mu \gamma \) are given. The dependence on the fermion masses is illustrated by comparing the hard bremsstrahlung corrections to different semi-leptonic channels.

We give an analytic formula for the double distribution of hadronic invariant mass and charged lepton energy to one-loop order of the perturbative QCD. Although infrared singular, this quantity is closely related to physical observables that can be obtained thereof through proper convolution.

The oblique part of the radiative corrections to the Left–Right model is described. The leading non-logarithmic terms are explicitly written. It is argued, on the basis of a comparison with the Standard Model, that one cannot use the loop contributions of the latter to refine phenomenological analyses of the Left–Right model, and by the same of any general extension.

We report on the analytical calculation of the \({\cal O}(\alpha _s^3)\) conversion factor between the \(\overline {\textrm {MS}}\) quark mass and the one defined in the so-called “Regularization Invariant” scheme.

In the unconstrained MSSM, we reanalyze the constraints on the phases of supersymmetric flavour conserving couplings that follow from the electron and neutron electric dipole moments. We find that the constraints become weak if at least one exchanged superpartner mass is \(\gt {\cal O}(1~{\rm TeV})\) or if we accept large cancellations among different contributions. However, such cancellations have no evident underlying symmetry principle. For light superpartners, models with small phases look like the easiest solution to the experimental EDM constraints. This conclusion becomes stronger the larger is the value of \(\tan \beta \). We discuss also the dependence of \(\varepsilon _K\), \(\Delta m_B\) and \(b\rightarrow s\gamma \) decay on those phases. We show that even in the absence of genuinely supersymmetric sources of CP violation MSSM contributions may affect the determination of the Kobayashi-Maskawa phase \(\delta _{\rm KM}\).

I discuss recent developments in the study of cosmological limits on the Minimal Supersymmetric Standard Model (MSSM). In particular, I focus on the effect of neutralino-stau coannihilation on the relic abundance of neutralinos, and I give examples where the cosmologically derived limits on the supersymmetric parameters are relaxed, and one example (CP violating phases) where they are not.

With the process \(e^-\gamma \rightarrow \tilde {\chi }_1^0 \tilde {e}_{\rm L\,/\,R}^- \rightarrow e^- \tilde {\chi }_1^0 \tilde {\chi }_1^0\) it is possible to constrain selectron masses above the kinematical limit of the pair production process in \(e^+e^-\) colliders. We investigate these mass ranges and discuss the possibility to test the renormalization group equations for the selectron masses.

We study the possibility to measure the masses of the selectrons in neutralino production at an \(e^+ e^-\) linear collider with polarized beams. The cross sections and polarization asymmetries of neutralinos with gaugino character strongly depend on the masses of the exchanged selectrons. If the usual GUT relations of the selectron masses in the MSSM are relaxed large effects are possible especially in the polarization asymmetries. These can be used to determine the masses of both selectrons.

A brief review of relativistic two-body equations in QED and their nonrelativistic reductions is presented, beginning with the atomic Dirac–Breit equation. The emphasis is on lepton-antilepton bound states (leptonium), with a look at possible extensions to quarkonium.

Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed.

A non traditional method to calculate multi-point Feynman functions is presented. In the approach, \(D\)-dimensional loop integrals defining a Feynman amplitude are not directly performed, but a system of linear differential equations for the Feynman amplitudes themselves is found. The solution of the differential equations provides then with the actual value of the amplitudes.

Three programs are presented for automatically generating and calculating Feynman diagrams: the diagrams are generated with FeynArts, algebraically simplified with FormCalc, and finally evaluated numerically using the LoopTools package. The calculations are performed analytically as far as possible, with results given in a form well suited for numerical evaluation. The latter is then straightforward using the implementations of the one-loop integrals in LoopTools.

I discuss the problem to what extent fundamental interactions determine the structure of spacetime. I show that when we are using only topological methods the spacetime should be modelled on an \({\bf R}\)-compact space. Demanding the existence of a differential structure substantially narrows the choice of possible models but the differential structure may not be unique. I also show by using the noncommutative geometry construction of the standard model that fundamental interactions determine the spacetime in the class of \({\bf R}\)-compact spaces. Fermions are essential for the process of determining the spacetime structure.

I discuss recent development in investigation of physical consequences of exotic differential structures on manifolds. I show, following T. Asselmayer, that corrections to the curvature after the change of differential structure produce a source like term in the Einstein equations. Then I give examples of topologically trivial spaces on which exotic differential structures act as a source of gravitational force even in the absence of matter.