Lev B. Okun

Charmonium and gluons

Afther the discovery of J/ψ and ψ′ mesons many other narrow resonances were found which represent various levels of a system called charmonium. In this review theoretical interpretation of charmonium properties is given. The classification of charmonium levels and their electromagnetic and strong decays are discussed. The basic assumption is that strong interaction between charmed quark and charmed antiquark in charmonium is mediated by coloured gluons as described by Quantum Chromodynamics (QCD). It is argued that charmonium is an ideal object to test the basic ideas of QCD. Both the traditional nonrelativistic approach to charmonium and the dispersion one are presented. The latter approach is free from many additional assumptions inherent to potential calculations. Other applications of QCD to the charmed world are briefly reviewed. Different parts of the review are addressed to different readers. It could, in particular, be of interest to students, specializing in elementary particle physics, experimentalists and theoreticians who are active in this field. The final results are presented in such a form as to follow for a direct comparison with corresponding experimental data.

Historical roots of gauge invariance

Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the so called Standard Model). The roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. Subsequent developments led to the discovery that different forms of the vector potential result in the same observable forces. The partial arbitrariness of the vector potential A brought forth various restrictions on it. div A = 0 was proposed by J. C. Maxwell; 4-div A = 0 was proposed L. V. Lorenz in the middle of 1860s . In most of the modern texts the latter condition is attributed to H. A. Lorentz, who half a century later was one of the key figures in the final formulation of classical electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged spinless particles was formulated by E. Schrodinger, O. Klein, and V. Fock. The latter discovered that this equation is invariant with respect to multiplication of the wave function by a phase factor exp(ieX/hc) with the accompanying additions to the scalar potential of -dX/cdt and to the vector potential of grad X. In 1929 H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-abelian gauge theories started in 1954 with the paper by C. N. Yang and R. L. Mills.

Violation of CP invariance

It has been discovered that long-lived neutral K-mesons decay into π + π − with a small relative width (B ∼ 2.10 −3 ). This discovery signified that decays of K 0 2 mesons violate CP invariance. Violation of CP invariance means if K 0 1 (K 0 2 ) denote the states with CP = + 1 (-1), the long-lived neutral K-meson is not identical to K 0 2 Phenomenologically, it is natural to distinguish between two possible mechanisms of CP violation in certain neutral K-mesons. There are various other CP-odd effects that have been described well by the mechanism of super weak mixing. All the CP-odd decays in the chapter are among certain K-mesons. In spite of a thorough search, no violation of CP was detected in decays or interactions of other particles. This exceptional behavior of certain K-mesons is based on the enhancement of CP-odd effects in certain K-decays.

Neutron-antineutron oscillations: Theoretical status and experimental prospects

This paper summarizes the relevant theoretical developments, outlines some ideas to improve experimental searches for free neutron-antineutron oscillations, and suggests avenues for future improvement in the experimental sensitivity.

Mass of the higgs versus fourth generation masses

The predicted value of the higgs mass mH is analyzed assuming the existence of the fourth generation of leptons (N, E) and quarks (U, D). The steep and flat directions are found in the five-dimensional parameter space: mH, mU, mD, mN, mE. The LEPTOP fit of the precision electroweak data is compatible (in particular) with mH∼ 300 GeV, mN∼50 GeV, mE∼100 GeV, mU+mD∼500 GeV, and |mU−mD|∼75 GeV. The quality of fits drastically improves when the data on b-and c-quark asymmetries and new NuTeV data on deep inelastic scattering are ignored.

Paradoxes of unstable electron

Abstract The hypothesis that an electron is unstable — when we try to make it consistent with the vanishing mass of the photon-leads to a number of paradoxical statements. The lifetime of the electron is determined by emission of a huge number of longitudinal photons and depends exponentially on the amount of emitted energy. This suggests to discuss searches for charge nonconservation in experiments with high energy particles.

REAL AND VIRTUAL PHOTONS IN WEAK LEPTONIC PROCESSES AT HIGH ENERGIES.

Abstract Weak-electromagnetic processes in colliding ee(eμ, μμ) beams at high energy are discussed (E ≈ 2 × 200 GeV). Radiative and higher order weak corrections to the amplitude of reaction e + e − → ν ν γ are considered. The interference between weak and electromagnetic amplitudes of e + e − scattering and e + e − → μ + μ − annihilation is calculated. The formulae obtained are applicable also to the muon induced reactions. The logarithmic terms in radiative corrections to cross sections of the above processes are calculated. The corrections to the weak amplitudes due to the hadron contribution are discussed.

Sum rules for the decays of the c-even charmonium states

Abstract Sum rules for the decays of the C -even charmonium levels ( 1 S 0 , 3 P 0 , 3 P 2 , 1 D 2 ) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J PC =0 −+ ,0 ++ ,2 ++ ,2 −+ . The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.

Z lineshape versus fourth-generation masses

AbstractThe dependence of the Z-resonance shape on the location of the threshold of the N