The hierarchy problem in the mass of the Higgs Boson
Lim, Zhi Yong
Date of Issue2018
School of Physical and Mathematical Sciences
The key question addressed in this thesis is the little hierarchy problem and the concepts of naturalness, and how supersymmetry solves it. The hierarchy problem is connected to the problems of naturalness and fine-tuning, which examine how much parameters within a theory can vary such that the theory will still be natural. The criterion used will be the Barbieri-Giudice measure, as a way of quantitatively measuring the amount of fine-tuning, although that has its problems. Supersymmetry introduces a bosonic-fermionic symmetry, where there exists a transformation operator that changes bosonic to fermionic states and vice versa. Considering the couplings of the Higgs bosons to the particle content of the Standard Model (SM) and the Minimal Supersymmetric Model (MSSM), the quadratic divergence vanishes and the leading order becomes a logarithmic divergence, which is more manageable, i.e.\ less fine-tuning will be involved. This thesis introduces the key techniques in constructing the SM, namely spontaneous symmetry breaking and renormalization. The basic rules of Feynman diagrams are also introduced within the context of the Standard Model. With this, the MSSM is introduced, applying the techniques described above. These superpartners are shown to produce radiative corrections that cancel out those of the SM particles, which removes the quadratic dependence on the scale of the theory. The corrections are calculated directly with the Feynman diagrams, using the cutoff regularization so that the cancellation is explicit. Then, the mixing between the top quarks and stop squarks are added for a fuller picture.
Final Year Project (FYP)