Effective field theory from phenomenology to extra dimensions

This thesis incorporates four projects ranging from phenomenological studies of kaons and B mesons to the more theoretical Randall-Sundrum scenario. We study the weak decay of the charged kaon to a charged pion and neutrinos. We find a correction to the calculation of the branching ratio of this decay due to QCD effects near the charm scale contributing to the theoretical uncertainty in this calculation. We then study a model with a SU (2)_L x SU (2) _R x U(1) gauge symmetry which has purely right handed couplings in the third generation of quarks. By examining the constraints on this model from B and K decays, neutral meson mixing and CP violating observables we find that such a model can not be ruled out. We examine the consequences of this model for neutral B decays to CP eigenstates. We then turn to the study of the compactified extra-dimensional Randall-Sundrum scenario. In an effort to determine the stability of the hierarchy in this scenario we study the theory at the classical level to all orders in perturbation theory. We consider the scenario in the case of the most general action involving a bulk scalar field and gravity incorporating all higher derivative operators. We find that the hierarchy is stable to all orders in the perturbative expansion. Finally, we develop a procedure where we match the RS1 theory to an effective theory with smaller extra-dimensional size. In a theory with a bulk scalar field, couplings on the hidden brane are found to flow with the radius of the space in a renormalization group sense. We employ this technique in studying the stability of the Randall-Sundrum hierarchy.