In this thesis I discuss different aspects of high energy resummation in Quantum Chromo-Dynamics and its relevance for precision physics at hadron colliders. The high energy factorisation theorem is presented and discussed in detail, emphasizing its connections with standard factorisation of collinear singularities. The DGLAP and the BFKL equations are presented and leading twist duality relations between the evolution kernels are discussed. High energy factorisation is used to compute resummed coefficient functions for hadronic processes relevant for LHC phenomenology. The case of heavy flavour production is analysed in some detail and results already present in the literature are confirmed. High energy effects can play an important role for such cross sections which are to be used as standard candles at the LHC, such as W/Z production. To this purpose Drell-Yan processes are studied in high energy factorisation. The inclusive cross section for Higgs boson production via gluon-gluon fusion is analysed both in the heavy top limit and for finite values of the top mass. The different high energy behaviour of the two cases is studied, showing explicitly that the full theory exhibits single high energy logarithms in contrast to the infinite top mass limit. The correct high energy behaviour of the partonic cross section is then combined to the NNLO calculation performed in the heavy top limit, in order to obtain an improved coefficient function. Finite top mass effects at high energy on the hadronic cross section are moderate. As far as parton evolution is concerned, an approximate expression for the NNLO contribution to the kernel of the BFKL equation is computed exploiting running coupling duality relations between DGLAP and BFKL. This result includes all collinear and anticollinear singular contributions and it is computed in various factorisation schemes. The collinear approximation is tested against the known LO and NLO kernels with the discrepancy being at the percent level. Therefore the approximate NNLO contribution is likely to be close to the as yet unknown complete result in the region relevant at leading twist.

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We present measurements of partial branching fractions for the inclusive semileptonic decay of B ! Xu` (` = e or ) leading to the determination of the CKM matrix element jVubj. This analysis is based on a sample of 460 million BB events recorded at the (4S) resonance at the BABAR detector. We select B ! Xu` events using the energy spectrum of the lepton (E`) in an event where one of the B-mesons is fully reconstructed. We measure partial branching fractions in restricted regions of the E` spectrum, which are translated into values of jVubj using four theoretical approaches. We calculate the arithmetic mean, using the results from the four theoretical approaches at E` > 1:5 GeV resulting in: jVubj = (4:68+0:31 0:32) 10 3. The analysis presented in this thesis is the rst time a measurement of jVubj has been performed using the E` spectrum in events tagged with a fully reconstructed B meson.

This thesis presents measurements of isolated photon production in deep inelastic ep scattering made with the ZEUS detector at HERA using an integrated luminosity of 320 pb-1. Measurements were made in the isolated-photon transverse-energy and pseudorapidity ranges 4 < E_T < 15 GeV and -0.7 < eta < 0.9 for exchanged photon virtualities, Q^2, in the range 10 < Q^2 < 350 GeV^2 and for invariant masses of the hadronic system W_X > 5 GeV. Differential cross sections are presented for inclusive isolated photon production as functions of Q^2, x, E_T and eta. Leading-logarithm parton-shower Monte Carlo simulations and perturbative QCD predictions give a reasonable description of the data over most of the kinematic range. To increase the precision of the measurement, a study was undertaken to improve the Monte Carlo description of electromagnetic showering in the ZEUS calorimeter. This utilised isolated electromagnetic clusters from ZEUS data to which Monte Carlo event samples with varying parameters for electromagnetic showering were fitted. These improvements have been adopted in the standard ZEUS detector simulation and were also shown to improve electron identification. For the main isolated photon analysis a range of methodologies for photon clustering and identification, isolation and signal extraction were investigated and the optimal methods were chosen. As a result of these refinements and the improved electromagnetic shower modelling, the systematic errors decreased significantly, typically by a factor of three when compared to the same phase space in the previous ZEUS publication. In addition the luminosity was increased threefold and the phase space was expanded. These two improvements brought about a factor three reduction in statistical uncertainty.

The present thesis consists of two parts. The first part is devoted to the analysis of discretizations of a class of basic electronic density functionals. In the second part we suggest and analyze Quasicontinuum Methods for an atomistic interaction potential that is based on a field. We begin by formulating and analyzing a model for the study of finite clusters of atoms or localized defects in infinite crystals based on a version of the classical Thomas{Fermi{Dirac{von Weizs?acker density functional. We show that the resulting constrained optimization problem has a minimizer and we provide a careful analysis of the solvability of the associated Euler{Lagrange equation. Based on these results, and using tools from saddle-point theory and nonlinear analysis, we then show that a Galerkin discretization has a solution that converges to the correct limit (in the case of Dirichlet as well as periodic boundary conditions). Furthermore, we investigate the issue of optimal convergence rates. Using appropriate dual problems, we can show faster convergence for the energy, the Lagrange multiplier of the underlying minimization problem, and the L2-errors of the solutions. We also look at the dependence of the density functional on the nucleus coordinates and show a convergence result for minimizing nucleus configurations. These results are subsequently generalized to the case of discretizations with numerical integration. Existence and convergence of solutions, as well as optimal convergence rates can be established if quadrature rules of sufficiently high order are applied. In the second part of the thesis we consider an atomistic interaction potential in one dimension given through a minimization problem, which gives rise to a field. The forces on atoms are in this case given by local expressions involving this field. A convenient feature of this model is the existence of a weak formulation for the forces, which provides a natural connection point for the coupling with a continuum model. We suggest Quasicontinuum-like coupling mechanisms that are based on a decomposition of the domain into an atomistic and a continuum region. In the continuum region we use an approximation based on the Cauchy{ Born rule. In the atomistic subdomain a version of the atomistic model with Dirichlet boundary conditions is applied. Special attention has to be paid to the dependence of the atomistic subproblem on the boundary and the boundary conditions. Applying concepts from nonlinear analysis we show existence and convergence of solutions to the Quasicontinuum approximation.

The LHCb experiment at the CERN LHC accelerator will begin physics data taking in late 2009. LHCb aims to discover New Physics processes via precision measurements using heavy flavoured hadrons, such as B and D hadrons. This thesis describes studies relevant to measurements of B decays to hadronic final states at LHCb. The Ring Imaging Cherenkov (RICH) counters of LHCb are crucial to the performance of such measurements. They use arrays of Hybrid Photon Detectors (HPDs) as their photodetection system. Detailed results are presented from the characterisation programme of the entire sample of 557 HPDs that were produced. Their overall performance is found to be outstanding, with only 2.2% of HPDs judged to be unusable for the RICHes. The LHCb requirements and the contractual specifications are met and often exceeded in key areas. The measurement of the single photoelectron detection efficiency, eta, of the HPD anode is described in detail. The efficiency was measured as eta = (87.9 +/- 1.4)%. This value exceeds the LHCb-RICH requirement, and is in agreement with previous measurements. A method to measure the detector proper time resolution for two-body hadronic B decays from data, making use of the per-event proper time error, is described. A proper time resolution model is proposed and is shown to accurately match the simulated resolution for these decays. The model parameters can be measured on data by fitting the flavour-tagged proper time distribution of the Bs->K-Pi+ decay. Constraining the proper time resolution model via this method can potentially reduce systematic errors in time-dependent studies. A study is presented which examines the prospects of LHCb to discover new baryonic B decay modes, with particular focus on the experimentally most promising mode, Bd->ppbar. It is found that a 5 sigma discovery of Bd->ppbar is possible with only 0.25 fb^-1 of nominal LHCb data, if its true branching fraction is close to the current experimental upper limit. Finally, the prospects of LHCb to measure the direct and mixing-induced CP asymmetries for the decay Bd->Pi+Pi-, via a time-dependent study, are assessed. A fit is made to the invariant mass and proper time distributions of simulated data. The total sensitivities with early data (0.3 fb^-1) are found to be 0.135(stat) + 0.012(syst) and 0.093(stat) + 0.018(syst) for the direct and mixing-induced asymmetries respectively. These sensitivities are competitive with current experimental measurements, and indicate that LHCb will come to dominate the world average values for these CP asymmetries as more data is collected.

This work presents the first ever measurements of several polarization observables for the reactions gamman->K0Lambda and gamman->K0Sigma0.

The mineral β-tricalcium phosphate (β-TCP), Ca3(PO4)2, is currently of interest in the immobilisation of nuclear wastes, along with various biomedical applications. Several substituted forms of β-tricalcium phosphate have been produced with the general formula Ca9M3+ x (PO4) 6+x, where M3+ is a trivalent metal ion, with Ga, Al and La being the main focus of study here, and x generally falling between 0 and 1. The aim of this study has been to investigate the substitution mechanisms of ions into β-tricalcium phosphate along with the effects which substitution has on its structure. This has mainly been carried out by nuclear magnetic resonance on many of the available nuclei, along with x-ray and neutron diffraction of the materials produced. It has been shown that substituted β-tricalcium phosphate can be readily produced, although with additional phases present in some samples, generally upon high levels of substitution, and especially in the Al case. Rietveld refinements of x-ray and neutron diffraction patterns show the β-TCP structure remains intact throughout the samples produced, with Ga thought to substitute onto the Ca(5) site, La onto the Ca(3) site and Al onto both the Ca(4) and Ca(5) sites. However, values determined for the Ca site occupancies have in some cases deviated from those expected and often have large errors associated with them. Part of this is due to problems with the peak shape used with the x-ray diffraction data, but it is also thought that disorder may be present in the substituted samples, causing unexpected values in the refinements. Total correlation functions have also been produced from the neutron diffraction data and again show the β-TCP structure to remain relatively unchanged in most cases with 6-coordinated Al and Ga present in samples containing those ions. The addition of Al does, however, change the structure considerably, possibly through distortions of the sites involved due to the smaller size of the Al ions. 31P NMR has been performed on all samples and appears extremely sensitive to changes in the Ca site occupancies. Fitting has been performed on spectra from the Ga system, with fits produced consistent with substitution onto the Ca(5) site. The method of substitution for the Al and La systems has proven to be too complex for fitting of the 31P spectra to be practical in these cases. Natural abundance 43Ca NMR has been performed on some of the samples and, although having poor signal to noise ratios, the spectra produced can be fitted according to the method of site substitution predicted. 27Al NMR on the Al containing samples has produced interesting spectra, with an additional feature being present in addition to the expected 6-coordinated resonance. This feature lies within the range associated with AlO6 or Al(OP)5 environments and is thought to be due to distortion of one of the Ca sites that the Al is substituting into, probably the smaller Ca(4) site.

Energy-scanned photoelectron diffraction was used to determine the local adsorption site of several molecular species on well defined single crystal surfaces. Cytosine and uracil on Cu(110) were found to adsorb with their molecular planes perpendicular to the surface and mostly aligned along the close packed [110] direction. Both molecules were found to adsorb through their constituent oxygen atom(s) and a deprotonated nitrogen atom. The associated Cu-O and Cu-N bond lengths were found to be 1.94 (+0.06/-0.04)Å and 1.94 (+0.07 / -0.03) Å, respectively, for cytosine and 1.96 ± 0.04 / 1.93 ± 0.04 Å and 1.96 ± 0.04 Å, respectively, for uracil. The mono- and bi- tartrate phases of tartaric acid on Cu(110) were found to adsorb via deprotonated carboxylic acid groups with the oxygen atoms in different near-atop sites. The associated Cu-O bond lengths were found to be 1.92 ± 0.08 Å / 1.93 ± 0.06 Å and 1.93 – 1.97 ± 0.06 – 0.09 Å respectively. Glycine on Cu(111) was found to adsorb via both its nitrogen and oxygen constituent atoms, though three competing models were found for the local adsorption site of the oxygen atoms. The nitrogen atom was found to adsorb in a near-atop site with an associated Cu-N bond length of 2.02 ± 0.03 Å. The oxygen adsorption site was found to at least have some near-atop characteristics, with the near-atop site having an associated Cu-O bond length of 2.00 – 2.02 ± 0.04 – 0.07 Å. Reanalysis of the C 1s PhD data of the hydrocarbon remnant from the decomposition of furan on Pd(111) found that the lowest energy model predicted by DFT does not occur, at least in large quantities, on the surface. The most likely structure was found to be CH–C–CH2. On the Ru(0001) surface, dehydrogenation of methanol was not observed in the temperature range around 150 K, with no evidence for the strong modulations in the O 1s PhD spectra predicted for a methoxy species. A reexamination of water adsorption of the rutile TiO2(110) surface found that water does, at least partially, dissociate on the perfect surface as well as at defect sites – in contrast to previously published experimental results. The associated Ti-O bond lengths for the resulting atop and bridging hydroxyl species were found to be 1.85 ± 0.08 Å and 1.94 ±0.07 Å respectively. Finally vanadyl phthalocyanine was found to adsorb upright (with the oxygen atom further from the surface than the vanadium atom) on the Au(111) surface. The V=O bond length was found to be 1.60 ± 0.04 Å.

The purpose of work was to obtain gold and possible other negative ion cluster beams where each constituent atom in the cluster carried an energy ≤ 1 keV, using the floating low energy ion gun (FLIGTM), and to test these in secondary ion mass spectrometry. The heavy negative metal cluster is worth researching because (i) there is the possibility of generating high secondary ion/sputter yields, and (ii) negative ions would be useful for insulators. The sputter cluster ion source (SCIS) developed in the University of Antwerp (Belgium) was selected because it can emit cluster ions of pure materials as well as compounds. Gold was chosen due to its high mass and thus high sputter rate. The source was retrofitted to a FLIG column by designing matched ion optics based on simulation, a new mass separator, vacuum devices and power supplies. The ion gun of SCIS-FLIG was then tested and characterised, and defects were improved. As the result, ultra low energy gold cluster ions were obtained for the first time. The ratio of IAu1-:IAu2-:IAu3- is about 13:1.2:1, and a maximum 1 keV Au1 – current density of 38 μA cm-2 was obtained at the sample, which is superior to any reported negative gold cluster ions source. Ions with higher energy (up to 3.7 keV) and positive ions were also obtained. A preliminary study of the usefulness of the gold cluster ions in SIMS depth profiling with a silicon sample was conducted afterwards. Nonlinear sputtering with E0 ≤ 1 keV was observed for the first time. The sputter rates of the ions are higher than that of O2 + and Cs+. Gold deposition due to Au3 – bombardment (E0 = 0.33 keV) was observed at a dose ≤ 0.54×1017 cm-2, otherwise sputtering can be achieved with dose ≥ 1×1017 cm-2. A peculiar observation is the time dependent evolution of the bombarded silicon surface during subsequent atmospheric exposure. Further work in obtaining a more reliable and long-lived source and a higher current density at the sample is recommended.