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In this thesis I have corroborated earlier findings showing that in a one-dimensional system we have a direct correspondence between some of the physical properties of bosons and fermions. I have shown there is a very good agreement with the length of two-body correlations between a many body Bose system and an exact Fermi system in one dimension. I have also calculated the energy per particle of the Bose system and found that as we approach the Tonk–Girardeau regime of impenetrable bosons that this energy is comparable to the kinetic energy of a non-interacting Fermi gas. The point-like interaction or hard-core condition acts like a pseudo-Pauli exclusion principle in the Bose system. As we decrease the density the interaction potential becomes negligible and we find an almost direct agreement with the kinetic energy of the Bose fluid and the kinetic energy of a system of non-interacting fermions. In high density regimes we find that we have a direct agreement with the mean field approximation and as we tend to low density systems we see that our energy levels cross over to those determined by Fermi statistics. The results gained within the hypernetted-chain scheme show a direct relationship with those gained within the framework of the Quantum Monte Carlo simulations for the same system of impenetrable bosons. We go on to develop further analytical models in one-dimension, including a ring of spinless fermions or Josephson Junctions and to calculate ground state energies and subsequent currents induced. Here we find Aharonov–Bohm oscillations in our one-dimensional investigation dependant on the magnetic flux applied to the systems studied.

The Thesis investigates the possible case that the Electroweak Symmetry Breaking is not due to a light, weakly interacting Higgs boson, but instead the Symmetry is broken by strongly interacting heavy resonances. In that case, the formalism of the Electroweak Chiral Lagrangian can be used as a model-independent way to construct a low-energy effective theory for the electroweak interactions and using the Pade unitarisation protocol, certain resonances can be predicted. The scattering of longitudinally polarized W bosons, one of which decays leptonically and the other hadronically, is used as a channel to probe the mechanism of the Electroweak Symmetry Breaking in the mass range of 600 GeV up to 2.4 TeV and for different resonance scenarios, including the case that there is no resonance in the spectrum. The reconstruction of the vector bosons is described and it is demonstrated that, by exploiting key features of the hadronic environment, the contribution from the background processes can be reduced in such a way that the ATLAS detector will be able to see interesting WW scattering events within the above mass range with 30 fb x of data and it will be also possible to distinguish among the different resonance scenarios. A key study of the present research is the measurement of the WW scattering cross-section and it has been calculated that a significant measurement will be achieved, for the most pessimistic scenario, with 80 fb l of data. Regarding the performance of the ATLAS detector, the Thesis focuses on the Level-2 Trigger for selecting interesting physics events. After a short introduction to the Trigger system of the detector, the concept of the Region of Interest is explained and a method for reducing its geometrical size is presented. The method is based on the information from the Electromagnetic Calorimeter and it will be demonstrated that the reduced size can improve the performance of the Level-2 Trigger in terms of execution time (58% faster) but also for track reconstruction (6% more efficient) in the Inner Detector, especially during the high luminosity phase of the LHC.

Two analyses are performed with the large samples of dielectron and dimuon events collected by the D0 experiment at the Fermilab Tevatron pp̄ collider. The dilepton transverse momentum (pT) distribution in Z/γ*→e⁺e⁻ production is a powerful probe of Quantum chromodynamics. Until now, this distribution has been measured with limited precision. An alternative variable, Φ*η, is proposed due to its relatively low susceptibility to detector effects. The Φ*η distribution of events with Z/γ*→e⁺e⁻ invariant masses between 70 and 110 GeV, is measured in three bins of dilepton rapidity. This measurement, with 7.3 fb⁻¹ of data, is significantly more precise than previous measurements of the pT distribution. A state-of-the-art QCD Monte Carlo program is in modest agreement with the data. Using 8.6 fb⁻¹ of data, the ZZ/γ*→vve⁺e⁻ and WZ/γ*→eve⁺e⁻ processes are studied, yielding production cross sections of, σ(pp̄→ZZ/γ*) = 1.64 ± 0.46 pb and σ(pp̄→WZ/γ*) = 4.46 ± 0.64 pb, for Z/γ*→e⁺e⁻ invariant masses between 60 and 130 GeV. These are in agreement with Standard Model predictions.

This thesis describes a data-driven technique for estimating the multijet background to Supersymmetry (SUSY) searches with no leptons using the ATLAS detector at the Large Hadron Collider. The technique is used to estimate multijet distributions in SUSY signal and control regions with 1 fb−1 of sqrt(s) = 7 TeV data collected by ATLAS in 2011. The systematic uncertainty on the estimates is reduced with the development and use of novel event shape triggers. Multijet estimates provided from the technique developed in this thesis are used by the ATLAS collaboration in several different SUSY searches.

A search for the neutral Higgs bosons,φ , of the Minimal Supersymmetric Standard Model (MSSM) decaying to τ pairs in proton-proton collisions at √s = 7 TeV is performed. The e + τ-jet final state is considered in data corresponding to 2.1 fb-1 of integrated luminosity collected by the Compact Muon Solenoid detector. The search is performed separately in the inclusive channel, sensitive to both gg → φ and gg → b [Symbol appears here. To view, please open pdf attachment]φ production, and the b-tagged channel which maximises sensitivity to gg → b [Symbol appears here. To view, please open pdf attachment]φ. No significant excess of events over the predicted Standard Model backgrounds is observed. Upper limits are set on the φ → + τ+τ- production cross section, σ(pp → φ+X) x B( φ → τ+τ- ). Cross sections greater than 18 and 1.3 pb are excluded at 95% confidence level for mA = 100 and mA = 400 GeV respectively. The limits are interpreted as constraints on tan β in the mhmax scenario of the MSSM: Values of tan β greater than 12 and 40 are excluded at 95% confidence level for mA = 100 and mA = 400 GeV respectively. The inclusive channel is found to have the greatest tan β sensitivity at large mA and the b-tagged channel to have greatest sensitivity at small mA. The τ-jet reconstruction is calibrated using Z → τ+τ- events. A measurement of the Z → τ+τ- cross section in the e + τ-jet final state using the same dataset as the Higgs search yields σ (pp → Z + X) . B(Z → τ+τ-) = 1.06+0.05 -0.04(stat.) ± 0.07(syst.) ± 0.05(lumi.) nb. The result is in good agreement with the Standard Model prediction of 0.972 ± 0.042 nb at next-to-next-to-leading order. This measurement provides a cross check of the methods used in the φ → τ+τ- search.

Limits on the Higgs production crosssection at the Tevatron were placed using data with an integrated luminosity of 2.4 fb−1 from CDF. Limits over a Higgs mass range between 110 GeV and 200 GeV were determined, by calculating a limit at ten mass points distributed over this region. The analysis exclusively searches for Higgs produced by top-quark mediated gluon fusion and then decaying in to two W bosons. Only leptonic decay channel software considered, such that the final event signature consists of ee, eu, or uu with missing energy from undetected neutrinos. After an evaluation of alternative techniques, a neural net was selected as the best method for increasing the sensitivity of the measurement. The BFGS neuralnet training technique was selected as the most efficient method. A Bayesian Likelihood technique was used to place limits on the observed Higgs production cross section, and an expected limit was calculated by running 10,000 pseudo experiments. The 160Ge V mass point was the most most sensitive, achieving an expected limit 4.1 times the Standard Model prediction cross sectionat a 95% Confidence Level. Observed limits are with in 1σ of the expected limit belowa mass point of 160 GeV. Above this, observed limits are higher than the expected limits, within 2σ. The lowest observed limit was also at MH=160 GeV with a limit of 6.85 times the Standard Model prediction at a 95% Confidence Level. A new method for increasing the sensitivity of the measurement was proposed and investigated, but unused in the analysis.

Little Higgs models offer an innovative solution of the naturalness problem of the Standard Model. These models contain new particles which cancel the quadratic divergences in the Higgs mass caused by the top, gauge and Higgs loops. These new particles contribute to loop induced interactions of the Higgs boson. The loop induced decays of the Higgs to gluon and photon pairs are examined in two Little Higgs models - the Littlest Higgs Model and the Schmaltz Model. The production of Higgs pairs from gluon fusion, which proceeds via heavy quark loops, is also examined in these models. Another idea considered is the multiple point principle (MPP) applied to the two Higgs doublet extension of the Standard Model. The MPP stipulates that the coupling constants will be tuned to allow the existence of a maximal number of degenerate vacua. This principle is shown to lead to a Peccei-Quinn type symmetry which naturally suppresses phenomenologically dangerous flavour changing neutral currents. Quasi-fixed points of the renormalization group are then used to derive predictions for the Higgs masses and couplings.

We present original calculations of standard model processes involving two weak bosons at NLO in QCD, and study related phenomenology with reference to Higgs boson and new physics searches at the LHC. We employ a new theoretical technique, D-dimensional generalised unitarity, to obtain the multi-particle, one-loop scattering amplitudes for the processes pp → W⁺W^- + 1j, pp → W⁺W^- + 2j, pp → W⁺W⁺ + 2j, and gg → W⁺W^-g. We consider the LHC phenomenology of: the W⁺W^- + n jets background to Higgs searches, for n = 0,1,2; the effects of anomalous tri-linear gauge couplings in WW and WZ production; the background W⁺W⁺ + 2j to new physics searches involving like-sign leptons; and a method of spin determination of new states in a scenario where conventional methods fail.

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