abstract

A stroboscopic maps approach for continuous dynamical systems has been elaborated and generalized. For an impulse perturbation, the map equivalent to a given equation can be found analytically for a large class of systems, in the limit of the impulse width going to 0. This technique can be used for analyzing dynamical systems in which the perturbation has an impulse form, or can be joined with the Generalized Modulated Kicks Approximation to model a system with continuous or noisy perturbation. The validity of a “naive” method of finding the map is discussed.

abstract

The \(N = 4\) Super Yang–Mills theory remains finite if mass terms for the scalars and fermion are introduced explicitly by hand provided these terms satisfy the mass-squared supertrace sum rule \[\sum _{J=0,\frac {1}{2}} {(-1)}^{2J+1} M^2_J(2J + 1) = 0.\] It is shown that the sum rule emerges from the elimination of quadratic divergences in the one-loop effective potential of the theory.

abstract

Features of top quark physics at high energies are reviewed and developed both from a conceptual and a practical point of view, with particular emphasis on future \(p \bar p\) and \(e^+e^-\) colliders. We study distributions and observables from which properties of the top quark can be determined. Dominant higher order corrections are taken into account and the spin structure of the various cross sections is discussed.

abstract

Fifth order, \(\mathcal {O}(\beta ^5)\), exact corrections to the non-singlet electron structure function in QED are presented. Calculations were performed in the leading logarithmic approximation using the ad hoc exponentiation prescription proposed by Jadach and Ward and a recurrence formula for the elements of the Jadach–Ward series. A comparison with existing third order, \(\mathcal {O}(\beta ^3)\), solutions is also presented. The three next elements of the Jadach–Ward series were calculated numerically and parametrized with an accuracy better than \(5 \cdot 10^{-6}\) in the range of \(x\) between 0.01 and 1.

abstract

The aim of this paper is to study the possibility of a non-linear mechanism of quark confinement. The sets of coupled equations for Dirac fields carrying colours and flavours are discussed. They contain non-linear self-interaction and mutual interaction terms of the same fractional form that was studied before for single Dirac fields (Phys. Lett. 71B, 357 (1977); Phys. Lett. 76B, 391 (1980); Acta Phys. Pol. B 12, 601 (1981)). It turns out that the only way of preventing creation of isolated coloured objects consists in breaking global colour symmetry. An explicit form of the symmetry breaking term is proposed (different from that used in Acta Phys. Pol. B 19, 203 (1988)), which implies that only white currents are conserved and the three colours are truly inseparable. Moreover, the new equations have the advantage of having strictly colour symmetric (white) solutions that correspond to an absolute minimum of the symmetry breaking term of energy.

abstract

We propose a model based on the MIT Bag Model for particles containing one heavy quark. We eliminate the colour electric and the colour magnetic energy terms in the mass formula, by replacing them by a renormalization of the constants of the model.

abstract

We present the results of the numerical weak coupling calculations of the distribution of the chromoelectric and chromomagnetic field around the static quark–antiquark pair. Comparison with the Monte Carlo data is also performed in an attempt to filter off lowest order perturbative part of the MC results.

abstract

The relativistic two-body wave equation proposed previously for a pair of one spin-l/2 particle and one spin-0 or spin-1 particle of equal masses is approximately specified to the case of slowly moving centre of mass of the pair (affected by external forces). A simple wave equation is found in the instance of a spin-0 constituent.

abstract

First, we recollect the model of algebraically composite Dirac-type particles, leading to three families of leptons and quarks as well as to two hypothetical families of Yukawa scalars. Then, we briefly discuss new hadrons involving colored quark-like Yukawa scalars as their constituents. When denoting such scalars by \(y\), these (colorless) hadrons are: \((y \bar y)\), \((q \bar y)\) (both with \(B = 0\), \(L = 0\)) and \((yyy)\), \((qyy)\), \((qqy)\) (all three with \(B = 1\), \(L = 0\)). The lowest-in-mass versions of them have the \(J^P(I)\)-signatures: \(0^+(0,1)\), \({}^1\!/\!{}_2\) \(^+(0,1)\) and \(0^-(\!\) \({}^3\!/\!{}_2\) \(\!)\), \({}^1\!/\!{}_2\) \(^+(\!\) \({}^1\!/\!{}_2\) \(\!)\), \(0^+(\!\) \({}^1\!/\!{}_2\) ) [or \(1^+(\!\) \({}^1\!/\!{}_2\) , \({}^3\!/\!{}_2\) \(\!)\)], respectively. Among them, \((q \bar y\)) may be the only states stable in strong interactions (for adequate masses).

abstract

Using the two-gluon exchange model of the pomeron, the total and differential cross-section for production of heavy quark–antiquark pairs (\(c \bar c\), \(b \bar b\), \(t \bar t\)) by double pomeron exchange in high energy proton–proton collisions is calculated. The results for production of heavy quark–antiquark pairs are compared with those for production of the Higgs boson in the same reaction.