If new heavy particles are discovered at the Large Hadron

Collider (LHC), we will need a way to distinguish among various

theoretical interpretations for the new physics beyond the Standard

Model (BSM). Models of BSM physics often predict specific relations

that must be satisfied by the couplings of the new particles. For

example, the coupling of the quark, Kaluza-Klein quark and

Kaluza-Klein gluon of the minimal Universal Extra Dimensions (mUED)

model must equal the strong coupling constant of QCD up to small

symmetry-breaking corrections that are radiatively generated. Using

computer simulations, I investigate the possible precision with which

one can measure this coupling at the LHC by examining like-sign dilepton

events that include additional hadronic jets and missing transverse

energy. To set bounds on the precision of a measurement of

the mUED strong coupling constant, I vary this constant away from

its predicted value and investigate the resulting change to the

number of events expected at the LHC. I show that a

measurement of the mUED strong coupling constant can be constrained

to ~5 - 25% provided the systematic uncertainty of the mUED

signal can be reduced.

We examine the constraints on the two Higgs doublet model (2HDM) due to the stability of the scalar potential and absence of Landau poles at energy scales below the Planck scale. We employ the most general 2HDM that incorporates an approximately Standard Model (SM) Higgs boson with a flavor-aligned Yukawa sector to eliminate potential tree-level Higgs-mediated flavor-changing neutral currents. Using basis independent techniques, we exhibit regimes of the 2HDM parameter space with a 125 GeV SM-like Higgs boson that is stable and perturbative up to the Planck scale. Implications for the heavy scalar spectrum are exhibited.

The most general 2HDM contains an extended Yukawa sector that includes new sources of flavor-changing neutral currents (FCNCs), which must be suppressed due to experimental bounds. The flavor-alignment ansatz asserts a proportionality between the Yukawa matrices that couple the up-type (down-type) fermions to the two respective Higgs doublet fields of the 2HDM, thereby eliminating FCNCs at tree-level. If flavor-alignment is imposed at a high energy scale, such as the Planck scale, tree-level FCNCs can be generated at the electroweak scale via renormalization group running. We determine the size of FCNCs that can be generated at the electroweak scale via Planck scale flavor-alignment, and use experimental bounds on flavor-changing observables to place constraints on the flavor-aligned 2HDM parameter space.

As our ability to probe the nature of the fundamental particles and their interactions improves with increasing particle collider data, we have more compelling reasons to explore models beyond the Standard Model (SM). Searches for new Higgs bosons of an extended Higgs sector beyond the SM at the Large Hadron Collider (LHC) can be interpreted in the framework of the two-Higgs-doublet model (2HDM). 2HDMs are among the simplest extensions extensions of the SM that yield interesting phenomenology. Understanding the pattern in which Higgs bosons couple to fermions is important for searches for Higgs bosons beyond the SM (BSM) and flavor physics. In this dissertation, we study two specific patterns of Yukawa couplings which are designed to provide a more general Yukawa framework than the common Z2-symmetric models, providing access to more 2HDM parameter space, while still controlling the potentially dangerous flavor changing neutral currents (FCNCs).

The first project presented demonstrates that Z2-symmetric models are too restrictive and experimentalists should not limit themselves to these specialized models. Instead, we should allow experiments to determine the nature of Yukawa couplings.In this work, we assume the Yukawa coupling matrices are flavor-diagonal and so proportional to the mass matrices. This model is known as the flavor-aligned 2HDM (A2HDM), of which Z2-symmetric models are a subset. To demonstrate this paradigm shift, we devised two scenarios in which we simultaneously fit two excesses for BSM scalars in LHC data within the A2HDM via parameter scans. We then present a few benchmark parameter points of interest to demonstrate what channels may reveal more information in future BSM Higgs boson searches.

In the second project, we work under the assumption that the 2HDM Yukawa matrices are of the four-texture form, with zeros in particular entries, and the parameters therein have a hierarchy in accordance with the fermion masses. This structure is motivated by the Cheng-Sher-like physical Yukawa couplings that it can produce, which enables small flavor-violating processes occur but systematically avoids current limits on FCNCs. We show that these models are phenomenologically viable and recast the calculation of the physical Yukawa couplings in a basis-independent formulation by rotating into the Higgs basis before assuming a particular structure for the Yukawa coupling matrices. Finally, we discuss the landscape of flavor-violating observables' predictions in this model, the landscape of their measurements, and the prospect of these channels to be measured at future high-energy particle colliders.