A tale of two standard model extensions

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University of Alabama Libraries

The Standard Model (SM) has provided physicists with a nearly complete effective description of the fundamental building blocks for the Universe. While several questions regarding the makeup of our Universe have been resolved, many still remain. One such question deals with the vast energy difference between the electroweak scale and Planck scale (O(1017GeV)). The origin of this large divide has physical implications affecting the running of the Higgs mass, as it receives quantum corrections that are quadratic. Affiliated with this large division of energy scales is an issue that came about upon detection of the Higgs boson at the Large Hadron Collider (LHC), which enabled us to infer the value of the Higgs self-coupling. As a result, the renormalization group equation for the Higgs self-coupling predicts a negative self-coupling at around energies of $10^9 - 10^{11} $ GeV. If true, this would indicate that our vacuum state is unstable. Taking our motivation from stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability, and the beta-function of the self-interaction for the Higgs becomes exponentially suppressed at high energies, showing that such class of theory never suffers from a vacuum instability. Another interesting question to consider, is what might be the origin of the large mass difference between the fundamental fermions? As will be shown, the fermion mass hierarchy can be explained through the use of our formalism developed in our setup of the "Domain-Wall Standard Model in a non-compact 5-dimensional space-time", where all the SM fields are localized in certain domains of the 5th dimension. Reproducing the hierarchy is contingent upon the localization positions of the fermions along the extra flat dimension. As a result of these different localization points, the effective 4-dimensional Kaluza-Klein mode gauge couplings become non-universal. This allows for the possibility of interesting experimental considerations which will be discussed. Flavor Changing Neutral Current constraints provide stringent bounds on our model, through these constraints we can glean information about the extra dimension. We have found two possibilities that satisfy these constraints: (1) the KK mode of the SM gauge bosons are extremely heavy and unlikely to be produced at the LHC, however future FCNC measurements can reveal the existence of these heavy modes. (2) the width of the localized SM fermions is very narrow, meaning the 4D KK mode gauge couplings are almost universal. In this case the FCNC constraints can be easily avoided, even for a KK gauge boson mass of order TeV. Such a light KK gauge boson can be discovered at the LHC in the near future.

Electronic Thesis or Dissertation
Theoretical physics, Particle physics