In this thesis, we use the Coleman-Weinberg effective potential for computing the radiative corrections to scalar masses in six simple models of the quantum field theory. We probe, for example, the theory of two scalar fields, simple generalizations of the Abelian Higgs model or some classic extensions of the Standard Model. A common feature of all the theories considered is the existence of (at least) two mass scales different in order of magnitude. Being motivated by the hierarchy problem, we study mainly the sensitivity of light scalar masses on the radiative corrections induced by the heavy fields in relevant Feynman loops. We demonstrate that while the masses of scalars with zero VEV obtain corrections proportional to the masses of the heavy fields, in theories with the spontaneous symmetry breakdown is the Higgs mass always governed by the corresponding ordering parameter, i.e., by its vacuum expectation value. For the Standard Model, understood as an effective field theory, this implies that the Higgs boson mass is as stable with respect to the effects of possible new physics on very high energies as the masses of the leptons, quarks, W and Z bosons. Powered by TCPDF (www.tcpdf.org)

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In this thesis, we study low energy capture reactions and neutron-deuteron elastic scattering using halo effective field theory (EFT). At low energy, EFT provides a general framework to analyze physical systems regarding as an expansion of short-distance over large distance scales. We provide a model-independent calculation for neutron capture on carbon-14, radiative capture of 3He-4He, radiative capture of 3H-4He, and neutrondeuteron (n-d) doublet channel elastic scattering using halo EFT. These reactions play a significant role in the carbon-nitrogen-oxygen (CNO) cycle, solar neutrino flux measurement, lithium production, and big bang nucleosynthesis (BBN) in the early universe. The cross section is calculated for radiative neutron capture in carbon-14 using halo EFT. This reaction is slowest in the CNO cycle, and it acts as a bottleneck in the production of heavier nuclei A greater than 14. The capture contribution is different from Brett-Wigner resonance because of interference between resonant and non-resonant contribution. Also, we calculated, electromagnetic form factors for one-neutron halo nuclei such as carbon-15, beryllium-11, and carbon-19 using EFT. The electromagnetic form factors depend on the nucleon separation energy, effective range, and the two-body current. The EFT expressions are presented to leading order (LO) for 15C and next-to-leading order (NLO) for 11Be and 19C. We also calculated astronomical Sactor for 3He-4He and 3H-4He radiative capture reactions. The low energy Sactor for these reactions are important to understand the Li problem and neutrino physics. At the LO, the capture amplitude contains the initial state swave strong and Coulomb interactions summed to all orders. The NLO contribution comes from non-perturbative Coulomb interaction. Our calculated astrophysical Sactor for 3He- 4He is slightly above the average compared to the other measurement and prediction but consistent within current error bars. The Sactor for 3H-4He is also compatible with the experimental extrapolation. Finally, we studied doublet channel n-d scattering using halo EFT. A two dimer halo EFT is developed to describe the virtual state and three-body bound state in n-d scattering. We show the connection between virtual state and three-body bound state using S-matrix analysis and phase shift analysis which is supported by the Efimov plots.

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Donoghue's effective field theory of quantum gravity is extended to include the interaction of massless particles. The collinear divergences which accompany massless particles are examined first in the context of QED and then in quantum gravity. A result of Weinberg is extended to show how these divergences vanish in the case of gravity. The scattering cross section for hypothetical massless scalar particles is computed first, because it is simpler, and the results are then extended to photons. Some terms in the cross section are shown to correspond to the Aichelburg-Sexl metric surrounding a massless particle and to quantum corrections to that metric. The scattering cross section is also applied to calculate quantum corrections to the bending of starlight, and though small, the result obtained is qualitatively different than in the classical case. Since effective field theory includes the low-energy degrees of freedom which generate collinear divergences, the results presented here will remain relevant in any future quantum theory of gravity.

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