We study light hadron phenomenology using Lattice QCD. We focus on the calculations of the light pseudoscalar quantities: masses, decay constants and B-parameters; in particular the calculation of the Kaon B-parameter, BK, which when combined with experimental results yields a constraint of the unitarity triangle apex. We describe a calculation with 2+1 dynamical flavours of Domain Wall Fermions on two lattice volumes, with a lattice spacing a = 0:1 fm. The Iwasaki gauge action was used with coupling beta = 2:13 and the extent of the fifth dimension was Ls = 16. Following a brief review of continuum QCD and Lattice QCD we describe the Domain Wall formalism and the lattice methods used to calculate physical quantities. We present results from the two simulations and make comparisons with next-to-leading order chiral perturbation theory. We study the region of validity of chiral perturbation theory and calculate the associated low energy constants. We find these to agree with phenomenological estimates and other lattice calculations. We calculate the physical decay constants and find them to be in relatively good agreement with experimental values. We present a renormalised value for BK which includes systematic error estimates.

This thesis is an investigation into the current bounds on the trilinear R–parity–violating couplings in the Minimal Supersymmetric Standard Model without R–parity conservation. The model is described, and its implications are discussed. Bounds on the couplings are obtained from leptonic and mesonic decay data, approximating mediating sfermions as much heavier than the decaying particles and assuming that only one set of couplings is non–zero for each decay. Those bounds from the purely leptonic decay data are compared to bounds from the LEP–II data, over a large range of sfermion masses. A potential signal of R–parity–violation at existing lepton colliders is calculated assuming that certain couplings are close to their bounds. The signal is found to be feasible and the backgrounds to the process are found to be negligible.