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A phenomenological study is made of several aspects of the standard model (and beyond) in the context of collider physics. These calculations are performed in the framework of Quantum Chromodynamics (QCD) and the standard Elec-troweak theory in an attempt to understand the underlying gauge theory more fully. In chapter 2, a precision QCD and electroweak calculation is performed to predict the high transverse-momentum distribution of the intermediate vector bosons produced in pṕ collisions. Calculated cross-sections are compared with data from the CERN collider and predictions are made for the Tevatron, LHC and SSC. Theoretical uncertainties, due to scale and structure function ambiguities, are estimated. In chapter 3, the equivalent photon approximation (or EPA) is studied at high energies to determine the accuracy of the approximation. An exact calculation of the process e + q → e + q + γ is performed and compared with an approximate calculation of the process γ+q → γ+q , where the initial-state photon is produced (using the EPA) from an initial-state electron. The test is carried out for the cases where the final-state electron are tagged and untagged. At high energies, the approximation is accurate to within 10%. In chapter 4, deep inelastic Compton scattering is investigated at energies of the HERA ep collider. A study of the production rate is made to determine the feasibility of measurement at HERA and it is clear that for pT < 50 GeV/c the cross-section will be measurable. In addition, studies are made to determine the efficiency of this process as a probe of the proton structure functions. The cross-section is only weakly dependent on the structure functions. In chapter 5, the production of charged Higgs scalars is considered at hadron colliders. The fully inclusive cross-section for charged Higgs scalars is calculated and compared with the associated W boson cross-section. The generic process g+b →b+t + t, which may proceed through an intermediate charged Higgs (or W) or through QCD processes, is studied and the Higgs cross-sections are compared with the W and QCD cross-sections.

The first measurement of the ratio of the W and Z cross sections in association with a single jet, known as the R_{Jets} measurement, is presented. The measurement was performed using 33pb^-1 of integrated luminosity, recorded during the year 2010 by the ATLAS detector at the LHC. At this time the LHC was operating at a center-of-mass energy of 7 TeV. The measurement is made as a function of the threshold on the jet transverse momentum, from 30 GeV up to a value of 200 GeV. The motivation for this measurement is outlined in terms of providing a stringent test of the Standard Model of particle physics, as well as a model independent tool for searching for new physics. Data driven tools are developed to perform the measurement and their performance is discussed. The result of the measurement is compared with the predictions of Next-to-Leading order perturbative QCD and found to be in good agreement over the entire range of transverse momenta considered.

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In this thesis, we study the "two-point approximation" for highly non-local effective actions, in the particular case of the Chiral Soliton Model of the nucleon. The nucleon in this model is regarded as being made of three valence quarks bound together by a meson field in a soliton form. Mesons are treated in mean field theory and the vacuum energy due to one-quark loops is included. The theory is defined with a finite cut-off in momentum space, consistent with an effective theory for the low-energy description of the strong interactions. We use the two-point approximation to calculate the vacuum correction to the chiral soliton energy for a variety of soliton profile functions, investigating the effect of different regularisation schemes. Results are little influenced by the choice of the cut-off, and are within 20% of exact calculations, done with the full inclusion of the Dirac sea. We then perform a dynamical calculation of the chiral soliton by including sea-quark effects self-consistently in the two-point approximation. We find a typical 20% (or less) deviation in the soliton energy from exact calculations. We apply a further "pole" approximation which leads to a significant algebraic simplification in the self-consistent equations. We show, in particular, that a simple numerical fit of the pole form to the two-point cut-off function yields essentially indistinguishable results from the latter. We finally calculate some static nucleon observables in the two-point approximation and find general agreement with exact calculations. In view of the results obtained, we may hope that the pole form of the twopoint approximation may prove to be a generally useful approach to similar problems involving highly non-local actions.

We investigate the dynamical generation of fermion mass in quantum electrodynamics (QED). This non-perturbative study is performed using a truncated set of Schwinger-Dyson equations for the fermion and the photon propagator. First, we study dynamical fermion mass generation in quenched QED with the Curtis-Pennington vertex, which satisfies the Ward-Takahashi identity and moreover ensures the multiplicative renormalizability of the fermion propagator. We apply bifurcation analysis to determine the critical point for a general covariant gauge. In the second part of this work we investigate the dynamical generation of fermion mass in full, unquenched QED. We develop a numerical method to solve the system of three coupled non-linear equations for the dynamical fermion mass, the fermion wavefunction renormalization and the photon renormalization function. Much care is taken to ensure the high accuracy of the solutions. Moreover, we discuss in detail the proper numerical cancellation of the quadratic divergence in the vacuum polarization integral and the requirement of using smooth approximations to the solutions. To achieve this, we improve the numerical method by introducing the Chebyshev expansion method. We apply this method to the bare vertex approximation to unquenched QED to determine the critical coupling for a variety of approximations. This culminates in the detailed, highly accurate, solution of the Schwinger-Dyson equations for dynamical fermion mass generation in QED including both, the photon renormalization function and the fermion wavefunction renormalization in a consistent way, in the bare vertex approximation and, for the first time, using improved vertices. We introduce new improvements to the numerical method, to achieve the accuracy necessary to avoid unphysical quadratic divergences in the vacuum polarization with the Ball-Chiu vertex.

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