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A Vμ disappearance analysis performed on the dataset collected during the first physics run of the T2K experiment is presented. This dataset represents an accumulated exposure of 3.23 x10¹⁹ protons on target (POT). A total of eight events passed all the selection criteria at the far detector, Super-Kamiokande, with an expectation of 22.8 ± 4.8(stat)+3.7-3.7(syst). A two flavor neutrino oscillation fit was performed with systematic uncertainties using a Markov Chain Monte Carlo method and a Bayesian approach. The sin² 2θ23 oscillation parameter was constrained to the physical region. Under these conditions, we found best fit values for the oscillation parameters of sin² 2θ23 = 0.83+016-0.18 and Δm²32 = 2.9+0.8-1.0 x 10⁻³ eV²/c⁴.

The measurements of two branching fraction ratios are reported in this thesis. The first one is a measurement of the ratio of the branching fractions for the decays B0s→ψ'Ø and B0s→J/ψØ. It is based on approximately 36 pb⁻¹ of data collected by the LHCb detector at √s = 7TeV during 2010. The result is 0.68 ± 0.10(stat) ± 0.09(syst) ± 0.07(B), which is compatible with previous measurements from experiments at the Tevatron. The second measurement is the ratio of the branching fractions for the decays B0s→Øμ⁺μ⁻ and B0s→J/ψØ as a function of the dimuon invariant mass. It is based on 1 fb⁻¹ of data collected by the LHCb detector at √s= 7TeV during 2011. The ratio of branching fractions is measured to be (0.558 ± 0.070(stat) ± 0.043(syst) ± 0.006(B)) x 10⁻³. Using the measured branching fraction of the decay J/ψ→μ⁺μ⁻ gives a branching fraction of B(B0s→Øμ⁺μ⁻) = (0.78 ± 0.10(stat) ± 0.06(syst) ± 0.28(B)) x 10⁻⁶. This is the most precise measurement of B(B0s→Øμ⁺μ⁻) and is in agreement with the Standard Model expectation.

In the present work we present a numerical and perturbation theoretic approach to the solution of the one-particle Schrödinger equation. The numerical methods developed can be used to find energy eigenvalues for one-dimensional problems as well as for radial ones. Expectation values are determined by an approach based on eigenvalue calculations, without the explicit use of wave functions. Hypervirial and Hellmann-Feynman theorems are used to obtain perturbation series to high order for polynomial type radial perturbations of the hydrogen atom. One such perturbation leads to an apparently new phenomenon in Rayleigh-Schrödinger perturbation theory. Wynn's algorithm is used to get Padé approximants for the perturbation series. The series for the energy and for the quantities < rᴺ > are treated, and both types of series can be found using the hypervirial method. Several applications of the numerical techniques are given; it is emphasized that theoretical manipulations are needed to transform the problem to an appropriate numerical form. It is demonstrated that a slight modification in the numerical techniques developed permits treatment of quasi-bound states as well as bound states. It is also shown how to calculate a local quantity Ψ(O), using energy calculations, and how to reduce the problem of treating angular terms in the quadratic Zeeman effect problem to a radial integration problem.

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For a full understanding of QCD and a precise comparison of the theory with experiment, QCD observables must be calculated to next-to-leading order in the strong coupling constant. This thesis will discuss some of the techniques used for calculating the one-loop Feynman diagrams which are required for such calculations, and their associated tensor integrals. In particular, conventional methods introduce Gram determinants. This can lead to unnecessarily complicated expressions and numerical instabilities in the limit of vanishing Gram determinant. An alternative method is presented which removes these problems by gathering together scalar integrals in combinations which are finite as the Gram determinant vanishes. These combinations are related to the corresponding scalar integrals in higher dimensions. This method is applied to the evaluation of the one-loop QcD corrections for the decay of an off-shell vector boson with vector couplings into two pairs of quarks of equal or unequal flavours. These matrix elements are required for the next-to-leading order corrections to four jet production in electron-positron annihilation, the production of a gauge boson and two jets in hadron-hadron collisions, and three jet production in lepton- nucleon scattering.

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