DOI: 10.7274/26231051.v1
title: Bounds on Gapped Continuum Spectra from Extra Dimensions

description: In this thesis the phenomenology of extra spatial dimension theories is explored through the application of what is known as a gapped continuum spectra. The gapped continuum framework under study considers one extra spatial dimension which is compact. This dimension consists of a single parameter denoted as ? that is directly related to the size of the dimension. In the limit that ? ? 8, the framework converges to the Standard Model (SM). This framework is easily applied to tree-level processes, as when calculating the amplitude by applying the rules for a Feynman diagram, the major difference between this framework and the SM is that the contribution from the mediator of the process is changed. As will be discussed in Chapter 1.3, the modification of the mediator depends on the center of mass energy, and the size of the dimension.
This thesis covers three major applications. The first application is implementing gapped continuum spectra calculations on Drell-Yan processes with dilepton or monolepton final states, as a study of ultraviolet (UV) to UV propagation with massive and massless gauge bosons. The second application is on proton-proton collisions resulting in a ditop final state, as a study of UV to infrared (IR) propgation with massless gauge bosons. The final application is on proton-proton collisions producing a single top quark final state in the t-channel, as a study of UV-IR propagation with massive gauge bosons.
In Chapter 2, the phenomenology of the Drell-Yan process is explored in detail. The Drell-Yan process at the Large Hadron Collider (LHC) can have the initial and final states considered to be massless. In the context of the framework, this places both the initial and final states on the UV brane. Under this framework, a bound is place on the size of the dimension to the 95% confidence level through the use of a ??2 calculation. In Chapter 3, the phenomenology of the ditop process is explored in detail. In contrast to the Drell-Yan process, while at the LHC the initial state can still be considered massless the final state of t ¯t is massive. In the context of the framework, this places the initial state on the UV brane, but the final state now lives on the IR brane. The modification to the mediator of the tree-level process, while still dependent upon the size of the dimension and the center of mass energy, is completely different from the modification seen in the Drell-Yan process. A bound on the size of the dimension in relation to the ditop process is also calculated to the 95% level. This bound places a maximum on the size of the extra dimension. Finally in Chapter 4, for the single top t-channel study, we outline the methodology for future work once relevant data has been experimentally gathered. The single top study starts with a mixed UV-IR initial state in contrast to both the DY and ditop studies, and ends with a UV-IR state. The propagation of the W boson in the process is UV-IR propagation as well. In the end, we will have placed the bound considering massive and massless UV-UV propagation, as well as massless UV-IR propagation, outlining the procedure for massive UV-IR propagation.
This bound provides a starting point for experimental searches for evidence of the extra dimension, as this bound is directly related to the mass gap of the continuum spectra of the gauge boson, and we will show how the cross section provides a meaningful way of observing the extra dimensional effects. These continuum modes are a direct search for physics beyond the Standard Model (BSM).