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We discuss the experimental signatures of new particles, predicted by the Standard Model and by super symmetry, in high energy proton-antiproton and, or, electron-positron colliders. A review of the theory of the Standard Model and of Supersymmetry, and a general discussion of collider physics are included. We review various Higgs boson production mechanisms, and consider one, Higgs boson production via Bremsstrahlung from electroweak gauge bosons, in detail. We find that the clearest signature is seen in the invariant mass distribution of the electron pair in the process ρρ → X (Z → He÷e־). However, the event rate is small, and, unless the Higgs boson can be identified from its decay products, such events may be misidentified as ordinary Z → e÷e־ events. We analyse UA1 jet-plus-large-missing-p┬ events in terms of a supersymmetric model with a light photino and with m≈ < m≈. If these events are due solely to scalar quark production, we find that, in our scenario, the scalar quarks must have a mass in the range 20 - 35 GeV, and the gluino mass must be greater than 0(60) GeV. We study the production of scalar electrons in e÷e־ collisions on and above the Z resonance. By calculating the cross-sections for e÷e־ → e÷eﻵﻵ־ we show that scalar electrons with mass above the beam energies (√s/2) can be identified. In particular, if a zino exists with mass m? < /s-m?. , then zino production and decay can give a contribution which dominates the ﻵ-exchange contributions. In this case the presence of both the ẽ and Ž may be revealed by a distinctive signature in the electron momentum distribution.

This work concerns the study of certain methods for investigating integrable systems, and the application of these methods to specific problems and examples. After introducing the notion of integrability in chapters 1 and 2, we go on, in chapter 3, to develop a novel type of discrete integrable equation by considering ways of enforcing Leibniz's rule for finite difference operators. We look at several approaches to the problem, derive some solutions and study several examples. Chapter 4 describes a numerical implementation of a method for solving initial value problems for an integrable equation in 2+1 dimensions, exploiting the integrability of the equation. The introduction of twisters enables a powerful scheme to be developed. In chapter 5 Darboux transformations derived from the factorisation of a scattering problem are examined, and a general operator form considered. The topic of chapter 6 is the relationship between the Darboux transform for the sine-Gordon and related equations and certain ansatze established by twistor methods. Finally in chapter 7 a geometric setting for partial differential equations is introduced and used to investigate the structure of Bäcklund transformations and generalised symmetries.

To investigate the effect in perturbative QCD of multigluon emissions on the transverse momentum distributions of multijet final states in electron-positron annihilation, we use a simplified model based on the approximation that gluons are emitted independently. As a guide to these multigluon emissions, we study the two-gluon contribution in some detail and calculate the Q(_T)-distribution for four-jet events in e(^+)e̅(^-)annihilation, using suitable jet-defining cuts, needed both theoretically, to regularize the soft- and collinear-gluon singularities, as well as experimentally, to group the final-state particles into distinct jets. To ascertain the accuracy of our approximate model, we compare our results with the exact ones, obtained by a Monte Carlo generation of events using the full matrix elements. We find that, for realistic values of the cuts, there is a significant kinematic region of agreement. This agreement and the validity of our model are further elaborated by taking its Abelian QCD limit, calculating distributions in other event shape variables and studying the jet broadening phenomenon. The applicability of our model is also delineated by finding it to be in remarkable structural and numerical agreement with the more exact algorithm of Altarelli et al. Finally, to investigate the effect of higher order and virtual graphs corrections to low order tree-level results, we use our model to calculate the O(a(^2)(_s)) Or-distribution for three-jet events in e(^+)e(^-) annihilation with virtual contributions included. We study the dependence of these corrections on the resolution parameters used to perform the (analytic) cancellation of infrared and collinear singularities between real and virtual graphs and discuss their physical consequences.